TJ 

870 

Z7 


WATER  TURBINES 

Contributions  to  Their  Study 
Computation  and  Design 


BY 

S.  J.  ZOWSKI 


Published  by 
The  Engineering  Society 

University  of  Michigan 


THE  AMERICAN  HIGH  SPEED  RUNNERS  FOR 
WATER  TURBINES 


Looking  at  a  modern  American  standard  runner  for  a  water 
turbine  one  is  liable  to  wonder  why  the  design  of  such  runners 
is  considered  to  be  one  of  the  most  difficult  problems  in  hydraulic 
engineering.  The  forms  of  the  runners  are  so  natural,  the  buck- 
ets and  their  curvature  so  simple,  that  "we  fail  to  see  where  the 
pretended  difficulties  are."  As  is  usual  in  such  cases,  we  forget 
here  again  that  there  is  always  a  direct  proportion  between  the 
simplicity  of  a  machine  and  the  amount  of  brainwork  and  time 
necessary  to  produce  the  same.  A  brief  history  of  the  evolution 
of  the  American  turbine  or  a  glance  at  the  reports  of  the  numer- 
ous tests  made  in  the  Holyoke  testing  flume  would  convince  us 
of  this  fact.  Indeed,  the  American  standard  runners,  as  they  are 
manufactured  now,  represent  a  great  amount  of  hard  and  earn- 
est work.  Hundreds  of  tedious  and  expensive  experiments,  with 
many  a  failure  and  success,  had  to  be  made — an  experience  of 
almost  half  a  century  had  to  be  aggregated  first,  before  this  mod- 
ern runner  type  was  produed. 

The  aim  was,  first,  of  course,  a  good  efficiency.  But  this  was 
not  all.  Already  in  the  early  eighties — at  a  time  when  the  Euro- 
pean engineers  still  were  questioning  the  advantages  of  the  radial 
inward  flow  turbine —  there  were  in  this  country  wheels  of  this 
type,  which  yielded  efficiencies  up  to  84%,  acording  to  the  tests 
made  in  Holyoke.  And  yet  since  that  time  remarkable  progress 
has  been  made.  Following  the  general  tendency  of  modern  en- 
gineering, the  speed  and  capacity  of  the  turbines  had  to  be  stead- 
ily increased.  That  for  the  turbine  designer  this  resulted  in  new 
difficulties  is  evident,  as  high  speed  calls  for  small  dimensions, 
while  high  capacity  calls  for  large  dimensions,  and  consequently 
the  increase  of  both  is  possible  only  to  a  certain  limit. 

The  purpose  of  this  study  is  to  show  how  far  the  American 
manufacturers  of  water  turbines  have  come  in  this  respec-t  and 
also  to  compare  the  results  which  were  obtained  by  their  various 


224635 


•in 


runner  types.  The  accuracy  of  this  study  is  naturally  limited  by 
the  accuracy  of  the  data,  which  were  accessible  to  the  writer, 
and  which  were  taken  from  the  guarantees  of  the  different  con- 
cerns. But  as  these  guarantees  are  based  on  careful  tests  made 
in  the  Holyoke  testing  flume,  and  as  these  tests  are  considered 
official  in  this  country,  also  the  results  of  the  following  study  can 
be  considered  reliable.  The  comparison  at  least  will  be  accurate, 
because,  if  mistakes  in  the  testing  of  the  wheels  be  made  (and 
some  engineers,  especially  in  Europe,  believe  that  the  Holyoke 
tests  are  not  quite  reliable  regarding  the  actual  discharge)  the 
same  mistakes  owuld  be  made  on  all  runners. 


NOTATION. 

To  get  a  proper  basis  for  this  study,  some  of  the  principal 
turbine  formulae  must  be  recalled  and  some  new  ones  derived. 
The  notation  is  the  same,  which  the  writer  uses  in  his  lectures  on 
water  turbines  at  the  University  of  Michigan. 

H-P  =  effective  power  of  the  runner. 

N  =  speed  of  the  runner  in  R.  P.  M. 

Q  =  discharge  of  the  runner  in  cubic  feet  per  second. 

H  —  net  head  in  feet  acting  upon  the  turbine  =  gross  head  minus  all 

losses  in  head  race,  conduit  and  tail-race. 
€  •=.  hydraulic  efficiency  of  the  turbine, 
(i — c)  H  =  head  lost  inside  of  turbine  itself  due  to  friction,  whirls 

and  shocks. 

Di  =.  mean  entrance  diameter  of  runner  in  feet. 
B  =  height  of  guide  case  in  feet. 

o-i  =  angle  between  entrance  speed  and  peripheal  speed  at  Di. 
&  =  bucket  angle  at  Di. 
Ci  =  real  entrance  speed  at  Di. 
Wi  =  relative  entrance  speed  at  Di. 
Vi  =  peripheral  speed  at  Di. 
CT  =.  radial  entrance  speed  at  Di  —  radial  component  of  c\,  see  Figs. 

I  and  2. 

SPEED. 

All  modern  American  runners  are  of  the  radial  inward  flow 
type,  working  with  pressurehead.  The  definition  of  the  "pres- 
surehead turbine"  or  "pressure  turbine"  (so-called  reaction  tur- 
bine) is:  "The  water  enters  the  runner  and  flows  through  the 
same  with  a  certain  pressurehead,  as  the  whole  available  head  is 
not  turned  into  speed  at  the  entrance.  The  real  entrance  speed 


—  5  — 

Ci  is  smaller  than  the  spouting  velocity.  A  pressurehead  is  left, 
to  be  used  for  the  acceleration  of  the  flow  of  the  water  through 
the  runner." 

The  regulation  of  the  hydrodynamic  conditions  in  the  runner, 
for  a  flow  either  with  or  without  pressurehead,  is  possible  by  the 
choice  of  the  angles  (3^  and  04. 

If  -the  entrance  into  the  runner  is  "shockless,"  and  the  dis- 
charge is  "perpendicular"  (real  discharge  speed  perpendicular 
to  the  corresponding  peripheral  speed)  then 


=  A  tgff  ~\ 
\          \ 


sin  (  8l  —  «! 


sin  (  ft .—  at )  ^ 

sz«  /3t    £0.s  % 

Both  ft  and  z/±  are  functions  of  the  angles  a±  and  /3±  for  a  given 
head.  The  speed  c±  can  naturally  never  exceed  the  spouting  ve- 
loicty  \/2geH.  It  would  become  equal  to  this  velocity  if 


\ 


sn        —  «x  cos  fl 
or  if 

ft  =  2at 

For  all  angles  /3i  which  are  larger  than  204,  the  speed  c1  will 
be  smaller  than  the  spouting  velocity,  hence  the  turbine  will  be  a 
pressure  turbine. 

For  a  pressureless  turbine  the  peripheral  speed  would  be 


This  is  variable  only  within  very  small  limits,  as  cosc^  varies  only 
a  little  for  the  values  of  at  which  are  used  in  practice.  Hence 
the  peripheral  speed  of  the  pressureless  turbine  is  practically 
given  by  the  head,  and  consequently  the  speed  N  (R.P.M.)  can 
be  varied  only  by  variation  of  the  runner  diameter  D±.  As  prac- 
tical reasons  restrict  both  the  increase  and  decrease  of  D1}  the 
speed  of  a  pressureless  turbine  is  variable  only  within  narrow 
limits.  This  is  one  of  the  main  reasons  why  nowdays  pressure 


—  6  — 

turbines  occupy  the  first  place,  and  pressureless  turbines  (Im- 
pulse wheels  and  Schwamkrug-turbines)  are  used  only  when  ab- 
solutely necessary.  The  speed  of  the  pressure  turbine  can  be 
varied  not  only  by  variation  of  the  runner  diameter  but  also,  and 
very  effectively,  by  variation  of  the  angles  ft  and  o±.  Combining 
both  means,  it  is  easy  to  vary  the  speed  of  a  pressure  turbine  for 
a  given  head  and  capacity  in  the  ratio  of  6  :  i. 

To  show  how  the  angles  Ol  and  ft  affect  the  peripheral  speed 
v   the  factor 


sin  (0i  —  ' 
sin  0i  cos 


of  equation  (2)  has  been  represented  by  a  series  of  curves.  Fig- 
ure 3  gives^the  values  of  this  factor  for  a  series  of  constant 
bucket  angles  ft  with  variable  angles  o±.  Figure  4  gives  the  same 
values  for  a  series  of  constant  angles  o±  with  variable  angles  ft. 
For  ft  =  90°  the  factor 


sin  (0!  —  aj 

=  i 

sin  0i  cos  «i 

for  all  values  of  04.  For  all  angles  ft  <  90°  the  value  of  the  rad- 
ical is  smaller  than  i ;  for  all  angles  ft  >  90°  its  value  is  larger 
than  i. 

As  a  low  or  medium  head  turbine  must,  as  a  rule,  be  designed 
for  a  relatively  high  speed,  all  American  standard  runners,  being 
built  for  low  or  medium  heads,  have  ft  >  90°  and  are  "high 
speed  runners"  Runners  with  ft  =  90°  are  called  "medium 
speed  runners"  and  those  with  ft  <  90°  are  called  "low  speed 
runners"  See  Figures  5,  6,  7. 

Practical  reasons,  as  for  instance  the  necessity  of  an  easy, 
smooth  and  yet  a  short  curvature  of  the  bucket,  are  limiting  the 
increase  of  ft.  The  value  of  ftmax  —  135°  will  represent  good 
practice  and  will  be  found  in  many  of  the  best  American  high 
speed  runners.  The  increase  of  angle  04  also  increases  the  speed 
z/i  for  all  angles  ft  >  90°.  But  to  avoid  what  is  called  over  gat- 
ing, it  is  advisable  not  to  assume  too  high  values  for  04.  Tests 
show  that  the  capacity  of  the  runner  reaches  its  maximum  at  a 
certain  gate  opening.  To  open  more,  is  not  only  useless,  but  even 


CO 


4 

d 


wrong,  as  not  only  the  output  goes  down,  but  also  the  efficiency. 
Although  the  point  of  overgating  may,  by  a  proper  design  of  the 
runner,  (at  the  least  passage  area)  be  moved  upwards,  it  is  not 
advisable  to  depend  on  this  too  much.  Less  efficiency  than  that 
expected  does  not  disappoint  the  turbine  buyer  as  much,  as  when 
the  turbine  is  found  to  give  less  than  the  expected  maximum 
power.  It  is  not  wise  to  make  04  larger  than  40°. 

The  hydraulic  efficiency  may  be  assumed  between  0.82  and 
0.84.     For  e  =  0.83,  V<#  =  5-167  and 


sin  (/?!  —  ax)         

-7—  \/  H 

sin  /?!  cos  a^ 

Since  for  a  given  runner  the  value  of  the  radical  is  a  constant,  we 
may  write 

and  Kv  may  be  called  the  "speed  constant." 

For  0!  =  135°,  ai  =  40°,  e  =  0.83,  Kv  =  about  7.0.  For  giv- 
en runners,  where  Dlf  H  and  N  are  known,  the  speed  constants 
may  be  calculated  as  follows : 


and  thus  the  different  runner  types  may  be  compared  in  reference 
to  speed.  These  constants  will  also  show,  whether  a  further  in- 
crease of  the  speed  is  possible  or  not.  Should  the  speed  constant 
be  considerably  larger  than  7,  then  it  can  be  assumed  with  certain- 
ty that  either  the  guaranteed  speed  is  higher  than  the  best  speed 
(the  best  speed  is  the  speed  at  which  the  runner  yields  the  max- 
imum efficiency)  or  that  the  nominal  diameter  of  the  runner  is 
larger  than  the  mean  diameter  Dr 

CAPACITY. 

The  quantity  of  water  discharging  from  a  given  opening  in  a 
certain  time,  say  in  one  sec.,  is  Q  =  const.  X  V^  if  H  is  the 
head  at  the  center  of  the  opening.  Hence,  for  a  given  opening, 


10  — 


Q/V//  =  constant.  We  call  this  constant  the  "specific  discharge" 
and  use  for  the  same  the  symbol: 

£1  =      =  cub.  ft.  /sec.  (5). 


The  specific  discharge  from  an  orifice  is  the  discharge  in  cub. 
feet  per  sec.  when  H  =  I  ft. 

Take  into  consideration  the  entrance  area  of  the  runner, 

Ai  =  *DiB  X  61, 

where  klt  being  smaller  than  i,  is  a  factor,  the  addition  of  which 
is  necessary,  in  order  to  consider  the  decrease  of  the  circumfer- 
ence by  the  ends  of  vanes  and  buckets. 

The  speed  of  the  stream,  normal  to  this  entrance  area,  is  the 
radial  speed  cr>  which,  like  all  speeds  of  a  given  runner  —  is  in  di- 
rect proportion  to  -\/H. 

Cr  =  fa  V/f 

Passage  area  X  speed  of  flow  normal  to  the  area  =  discharge. 
Therefore 

Q  =  A^Cr  =  TTD.Bk.k,  V//. 

Express  the  width  of  the  guide  case  in  parts  of  runner  diameter 

D, 

B  =  hDt 

(In  runners  of  the  same  type  k2  will  be  nearly  the  same  for  all 
runner  sizes.) 

Then  by  substitution  we  obtain 

Q  =  irDfktMH  =  K*DMH,  (6) 

where  Kq  =7rkik2ks. 

Q  Qi 

~ 


A2  ,/-//  -      A2  (7) 

Kq  is  the  "capacity  constant"  of  the  runner.  The  capacity  con- 
stant of  a  runner  is  its  specific  discharge  for  a  runner  diameter 
=  i  ft. 

In  all  runners  of  the  same  type  Kq  will  be  nearly  the  same, 
hence  the  capacity  constant  is  a  criterion  of  the  capacity  of  dif- 
ferent runner  types. 


FIG.  5. 
I.OW  SPEED  RUNNER. 


FIG.  6. 
MEDIUM  SPEED  RUNNER. 


FIG.  7. 
HIGH  SPEED  RUNNER. 


12   

SPEED  AND  CAPACITY. 

Knowing  the  speed  and  capacity  constants  of  different  runners 
and  runner  types,  we  are  not  yet  able  to  say  to  what  extent  they 
fulfill  the  requirements  of  highest  speed  zvith  highest  capacity. 

We  may  have  two  runners  with  two  different  values  of  Kq 
and  Kv,  and  yet  both  runners  may  be  equivalent,  when  we  con- 
sider capacity  and  speed  together.  Another  criterion  must  be  in- 
troduced, which  will  be  a  proper  combination  of  K^  and  Kv.  This 
•combination  could  be  made  in  various  ways,  but  the  most  conven- 
ient one  was  indicated  by  M.  Baashuus  and  Professor  Camerer 
and  may  be  derived  as  follows : 

7T   Dl  N  , 

*i  =    ~-    =  K-  V  H 


By  substitution  we  obtain 

"vi/~^        _  60  i/ET  X  Kv         \~7f_ 

7T  X    \     0, 


The  power  of  a  turbine  is 


550    J> 

efficiency  of  turbine.   H-P  =  KQH.     As   a   rule  r>  is   taken 
,  then  A:  =1/1  1. 

Q  =  H-P/KH,  and  Qt  =  H-P/KH  V// 
Substitute  in  the  last  equation  for  N,  then 


V  H-P 
whereby 

z%  _  60  l/Xq  AV  i/  A" 

"IT-  (9) 

J^t  may  be  called  the  "type  constant"  or  "type  characteristic"' 
of  the  runner.  It  is  a  combination  of  the  speed  and  capacity  con- 
stant, and  both  determine  the  type  of  the  runner.  The  conven- 
ience of  this  constant  will  be  apparent,  when  we  write  equation 
8  in  the  following  form : 


~ 


N  \/  H-P 

~ 


Kt  can  be  figured  directly  from  the  speed,  power  and  head, 
which  data  can  be  obtained  easily  and  seldom  differ  from  actual 
values.  No  dimensions  of  the  runner,  neither  the  discharge  nor 
the  efficiency  need  to  be  known,  and  yet  the  efficiency  is  consid- 
ered, because  the  formula 


Kt  = 


contains  K  which  is  a  function  of  rj. 

Turbines  of  the  same  capacity  and  speed  constant,  but  with 
different  efficiencies,  will  have  a  different  type  characteristic. 
Hence  Kt  is  an  absolute  criterion  for  turbines  in  reference  to  the 
aim,  "highest  speed  and  highest  capacity  with  best  efficiency!' 
The  meaning  of  Kt  can  be  found  by  assuming  H-P  =  i  and 


"The  type  characteristic  of  a  runner  is  the  speed  in  R.P.M. 
which  would  be  attained  by  the  runner,  if  it  were  reduced  in  all 
dimensions  to  such  an  extent,  as  to  develop  I  H-P  when  ^vor  king 
under  the  head  H  =  i  ft." 

In  Germany  the  term  "specific  speed"  (spezifische  Geschwin- 
digkeit  or  spezifische  Umlaufzahl)  and  the  symbol  Ns  or  ns  is 
used  for  Kt. 

The  writer  prefers,  however,  not  to  use  this  term  for  the  fol- 
lowing reasons.  The  word  specific  discharge  is  used  for  Q±  = 


—  14  — 

r,  the  word  specific  power  is  used  for  H-P/H^/H,  or  for 
the  discharge  and  power  under  the  head  H=i  ft.  Hence  spe- 
cific speed  should  denote  the  speed  at  H  =  i  ft. 

TV 

As  NI  is  used  very  frequently,  the  term  type  characteristic 
has  been  chosen  for  Kt. 

SPEED,    CAPACITY  AND   TYPE   CHARACTERISTICS    OF   THE    AMERICAN 
HIGH  SPEED  RUNNERS. 

I.      THE  DAYTON  GLOBE  IRON  WORKS   CO.,   DAYTON,   OHIO. 

The  Dayton  Globe  Iron  Works  Co.  is  the  manufacturer  of  the 
world  known  American  turbines.  The  last  two  types  developed 
by  this  concern  are  the  New  American  and  the  Improved  New 
American  turbine.  The  difference  in  the  design  of  these  two  run- 
ners is  seen  from  figures  No.  8,  9,  10,  n.  In  order  to  increase 
the  capacity,  the  height  has  been  increased,  and  the  entrance 
edge  inclined.  Thus  the  mean  diameter  D±  has  been  reduced  and 
speed  increased,  while  the  minimum  passage  area  at  "a"  is  kept 
ample.  The  discharge  end  of  the  bucket  has  also  been  changed. 
In  order  to  increase  the  actual  discharge  area,  and  to  so  decrease 
the  discharge  speed,  the  bucket  has  been  drawn  down  and  shaped 
spoonlike  at  the  discharge.  The  radius  of  the  curvature  of  the 
spoon  at  "b"  however  seems  to  be  rather  small.  The  outward 
discharge  could  be  made  more  effective  by  a  larger  spoon.  Nev- 
ertheless both  the  capacity  and  the  efficiency  of  this  runner  are 
very  good. 

The  data  for  a  19"  New  American  runner  are: 

H  =  2$  ft.    H-P  =  8o.    N  =  M9. 
60  Q  =  2128  cub.  ft.  per  min. 
(a)     Speed  constant. 

n.Ft...^.  *  PI  N        ^^7339 


— 
60  V  H 


60  1/25 
K*  =  5.62. 

Some  engineers  prefer  to  express  all  speeds  in  parts  of  the 
^pouting  velocity 


FIG.  8. 
SECTION  THROUGH  NEW  AMERICAN  RUNNER. 


FIG.  9. 
SECTION  THROUGH  IMPROVED  NEW  AMERICAN  RUNNER. 


FIG.  10. 
NEW  AMERICAN  RUNNER. 


FIG.  ii. 

IMPROVED   NEW   AMERICAN   RUNNER. 


Kv  =  about  0.7. 

(6)     Capacity  constant. 


0i  =  7.0933. 

<2i  7.0933     _ 

"" 


(c)     Type  characteristic. 

339 


Kt  = 


25  V7   25 


TABLE  NO.  i. 

NEW    AMERICAN    RUNNER. 


Di 

Ql 

H-P! 

Ni 

Kv 

Kci 

Kt 

K'v 

10 

1-95 

O.I76 

122.4 

5-35 

2.8l 

51.3 

0.667 

13 

2.96 

0.264 

99-o 

5-6i 

2.52 

50.9 

0.700 

16 

4.80 

0.432 

80.4 

5.6o 

2.70 

52.8 

0.699 

19 

7.09 

0.640 

67.8 

5-6i 

2.83 

54-2 

0.700 

22 

9.28 

0.840 

58.4 

5-60 

2.76 

53-5 

0.699 

25 

11.63 

1.048 

5i-4 

5.60 

2.68 

52.7 

0.699 

27-5 

15-04 

1.360 

46.6 

5-6o 

2.87 

54-4 

0.669 

30 

18.20 

1.648 

42.8 

5.6o 

2.90 

55-0 

0.699 

33 

21.60 

1.984 

39-2 

5.63 

2.85 

55-3 

0.703 

36 

27.50 

2.488 

35-8 

5-62 

3-05 

56-5 

0.702 

39 

29-83 

2.704 

32.8 

5-59 

2.82 

54-0 

0.697 

42 

3-024 

30.6 

5.60 

2.72 

53-2 

0.699 

45 

40.05 

3.624 

28.6 

5.60 

2.84 

54-5 

0.699 

48 

46.08 

4.080 

26.8 

5.6i 

2.88 

54-2 

0.700 

51 

49-27 

4.464 

25-4 

5.65 

2.72 

53-7 

0.705 

54 

57-93 

5.256 

23-8 

5.6i 

2.85 

54-5 

0.700 

57 

63-39 

5-744 

22.6 

5-6i 

2.81 

54-3 

0.700 

60 

73-73 

6.680 

22.0 

5-75 

2.85 

56.8 

0.717 

In  the  same  way  the  constants  for  the  other  runner  sizes  have 
been  calculated  and  are  given  in  Table  No.  i.  Also  the  specific 
speed  Nl  =  N/\/H  and  the  specific  power 

H-P  =  H-L_ 


-  i8  — 

have  been  added,  as  both  are  very  convenient  characteristics  of 
a  runner.  They  may  be  used  to  calculate  the  speed  and  power  of 
each  runner  for  any  given  head. 

JVi  =  339/V25  —  67.8. 
H-Pi  =  80/25  V25  =  0.64. 


[At  H  =  36  this  runner  would  have  a  speed  TV  =  67.8  X 
y  36  =  406.8  R.P.M.  and  would  develop  0.64  X  36  V36—  142.2 
H-P.] 

The  Improved  New  American  runner,  figured  in  the  same 
way,  will  be  found  to  have  a  speed  constant  which  is  considera- 
bly larger  than  that  corresponding  to  ^=135°  and  04  —  40°. 
As  the  speed  TV  (R.P.M.)  must  be  assumed  to  be  correct,  (is 
based  on  Holyoke  tests)  and  the  angles  /Jx  and  04  do  not  exceed 
135°  and  40°  respectively,  (^  is  about  135°  ;  ax  seldom  exceeds 
35°),  the  discrepancy  can  be  due  only  to  the  fact  that  the  nom- 
inal diameter  is  larger  than  the  mean  diameter  D^.  Measuring 
several  runners,  the  writer  has  found  that  the  nominal  diameter 
is  taken  close  to  the  fillet  (see  Fig.  No.  9).  The  ratio  of  the 
mean  to  the  nominal  diameter  was  found  to  be  about  0.97,  for 
smaller  runner  sizes.  For  larger  szes  this  ratio  is  somewhat 
smaller. 

TABLE  NO.  II. 

IMPROVED   NEW  AMERICAN   RUNNER. 


0i           <2i 

H-Pi 

Ni 

Kv 

K<i 

Kt 

K'v 

16            6.76 

0.616 

102.0 

6.88 

3-80 

80.  i 

0.858 

19            8.82 

0.808 

87.0 

6.96 

3-52 

78.3 

0.869 

22                11.63 

1.064 

75-0 

6.94 

3-47 

77-5 

0.866 

25                14.87 

1.360 

66.8 

7.04 

3.56 

77-9 

0.878 

29                19-74 

i.  808 

59-o 

7.18 

3.38 

79-4 

0.896 

34           26.83 

2.464 

49-8 

7-13 

3-35 

78.3 

0.890 

39           35-21 

3-232 

43-6 

7-15 

3-33 

78.5 

0.892 

44           44.63 

4.104 

38.8 

7.18 

3-32 

78.7 

0.896 

49           55-21 
54           69.08 

5-072 
6-344 

34-8 
31-6 

7.18 
7.18 

3-32 
3-41 

78.4 
79-5 

0.896 
0.896 

60           84.66 

s  s> 

7-784 

29.0 

7-30 

3-39 

81.0 

0.911 

66         101.80 

9-344 

26.2 

7.26 

3-35 

80.2 

0.905 

Table  No. 

II  has 

been  calculated  with  D,=c 

>-97  X 

nominal 

diameter  for  all  sizes. 

The  specific  power  and  speed  have  been  represented  by  curves, 
Fig.  12,  and  they  show  clearly  that  the  success  of  the  Improved 


10 


30  40  50 

FIG.  12. 


SPECIFIC  SPEED  AND  SPECIFIC  POWER  OF  THE  RUNNERS  MANUFACTURED  BY  THE 
DAYTON  GLOBE  IRON   WORKS  CO. 


N.  A.  —  NEW  AMERICAN  RUNNER. 

I.    N.  A.  —  IMPROVED  NEW  AMERICAN  RUNNER. 


—   20  — 

New  American  over  the  New  American  runner,  regarding  the 
aim  of  highest  capacity  and  highest  speed,  is  remarkable.  The 
dotted  curves  give  the  same  values,  if  the  nominal  diameters  are 
taken  as  a  basis. 

The  average  values  of  the  characteristic  constants  are : 

New  American  Improved  New  American 

Capacity  const.  A'a 2.8  3.43 

Speed  const.  Kv.....^ 5.6  7.1 

Type  characteristic  Kt 54.  i  79-0 


2. 


THE   PLATT   IRON   WORKS   CO.,   DAYTON,   Ov    SUCCESSORS   TO 

BIERCE   CO. 


To  meet  the  demand  of  turbines  for  low,  medium,  or  high 
heads,  this  company  is  manufacturing  both  radial  inward  and 
outward  flow,  pressure  and  pressureless  tubines.  Here  only  the 


IMG.  13. 

VICTOR  RUNNER,  TYPE  A,  INCREASED. CAPACITY. 

Victor  turbine  Type  A  for  low  and  medium  heads  will  be  taken 
into  consideration.  The  name  under  which  this  turbine  generally 
appears  is  Cylinder  Gate  Victor  Turbine,  as  this  concern  prefers 


Dj— »-  10 


7G 


FIG.  14. 


SPECIFIC  SPEED  AND  SPECIFIC  POWER  OF  THE  RUNNERS    MANUFACTURED  BY 
THE  PLATT  IRON  WORKS  CO. 

V.   S. — VICTOR  STANDARD  CAPACITY  RUNNER. 
V.  I.  C. — VICTOR  INCREASED  CAPACITY  RUNNER. 


—   22    

to  equip  its  turbines  with  the  cylinder  gate  regulating  device. 
There  are  two  patterns  of  the  Victor  runner  Type  A :  the  Stand- 
ard Capacity  and  the  Increased  Capacity  runner.  Both  have  the 
same  speed,  but  the  capacity  is  different. 

One  of  the  characteristic  features  of  the  Victor  runner  is  its 
large  number  of  buckets.  It  is  the  opinion  of  the  writer,  how- 
ever, that  there  are  no  reasons  to  use  so  many  buckets,  either  for 
strength  or  for  efficiency.  On  the  contrary,  it  is  advisable  to 
reduce  the  number  of  buckets  of  low  head  runners,  in  order  to 
increase  the  capacity  and  avoid  small  widths  of  the  chutes  at  the 
runner  hub.  Tables  III  and  IV  have  been  calculated  in  the  same 
way  as  the  preceding  tables. 

TABLE  NO.  III. 

VICTOR    RUNNER,    TYPE    A,    STANDARD    CAPACITY. 


Dl 

ft 

H-P* 

Ni 

K* 

K* 

Kt 

fC% 

12 

3-26 

0.296 

117.4 

6.13 

3-26 

63.8 

0.765 

15 

S.io 

0.462 

93-8 

6.13 

3-25 

63.7 

0.765 

18 

7-34 

0.666 

78.6 

6.18 

3-27 

64.2 

0.771 

21 

9-99 

0.906 

67.2 

6.15 

3-27 

64.0 

0.767 

24 

13-04 

1.183 

58.6 

6.12 

3-27 

63.7 

0.763 

27 

16.52 

1.498 

52.0 

6.  ii 

3-27 

63.7 

0.762 

30 

20.39 

1.849 

47-0 

6.14 

3-26 

64.0 

0.766 

33 

24-67 

2.237 

42.  & 

6.16 

3-26 

64.1 

0.768 

36 

29.36 

2.662 

39-0 

6.12 

3-26 

63.6 

0.763 

39 

34.46 

3-124 

36.0 

6.12 

3-25 

63.7 

0.763 

42 

39-97 

3.624 

33-6 

6.15 

3-27 

64.0 

0.767 

45 

45-88 

4.160 

31-2 

6.10 

3-26 

63.7 

0.761 

48 

52.20 

4.741 

29.0 

6.06 

3-25 

63.2 

0.756 

5i 

If'93 

5-341 

27.0 

6.00 

3-25 

62.5 

0.749 

54 

66.07 

5-990 

25.6 

6.01 

3.26 

62.7 

0.750 

57 
60 

73-61 
81.56 

6.673 
7-395 

24-4 
23.0 

6.07 
6.  02 

3-26 
3-26 

63.2 
62.7 

0-757 
0.751 

TABLE 

NO.  IV. 

VICTOR    RUNNER,   TYPE 

A,    INCREASED    CAPACITY. 

D, 

Qi 

H-Pt 

AT, 

Kv 

K* 

Kt 

K'v 

12 

3-59 

0.325 

117.4 

6.13 

3-59 

67.0 

0.765 

15 

5-6i 

0.508 

93-8 

6.13 

3.6o 

66.8 

0.765 

18 

8.07 

0.732 

78.6 

6.18 

3-6o 

67.2 

0.771 

21 

10.99 

0.996 

67.2 

6.15 

3.6o 

67.0 

0.767 

24 

14.35 

1.292 

58.6 

6.12 

3.59 

66.6 

0.763 

27 

30 
33 
36 
39 

18.17 
22.43 
27.14 
32.30 
37-91 

1.647 
2.036 
2.461 
2.928 
3.436 

52.0 
47-0 
42.8 
39-0 
36.0 

6.  ii 
6.14 
6.16 

6.12 
6.12 

3.58 
3.58 
3-59 
3-59 
3-59 

66.6 

67-1 
67.2 
66.8 
66.8 

0.762 
0.766 
0.768 
0.763 
0.763 

—  23  — 
TABLE   NO.   IV.— Continued. 

VICTOR  RUNNER,  TYPE  A,  INCREASED  CAPACITY. 


A 

& 

H-Pi 

tfi 

Kv 

K* 

Kt 

K'-i 

42 

43.96 

3.986 

33-6 

6.15 

3-59 

67.2 

0.767 

45 

50.46 

4-576 

31.2 

6.  10 

3-58 

66.7 

0.761 

48 

57-42 

5.206 

29.0 

6.06 

3-59 

66.2 

0.756 

Si 

64.82 

5.877 

27.0 

6.00 

3-57 

65.5 

0.749 

54 

72.68 

6.590 

25.6 

6.01 

3-59 

65.7 

0.750 

57 

80.97 

7-342 

24.4 

6.07 

3-58 

66.2 

0-757 

60 

89.72 

8.135 

23.0 

6.  02 

3-59 

65.6 

0.751 

The  average  values  of  the  characteristic  constants  are: 

Victor  Standard  Capacity    Victor  Increased  Capacity 
Capacity  const.  Kn  ................     3.26  3.59 

Speed  const.  Kv  ..................     6.1  6.1 

Type  characteristic  Kt  ............  63.5  66.6 


THE  JAMES  LEFFEL  AND  cov  SPRINGFIELD,  o. 

The  James  Leffel  &  Co.  manufacture  the  well  known  Double 
wheel,  designed  originally  by  James  Leffel  as  a  combination  of 
two  runners,  one  being  a  pure  radial,  the  other  a  radial  and  down- 
ward discharge  runner.  To  increase  the  capacity  this  runner  had 
to  be  bulged  out  more,  and  so  the  new  Double  wheel  was  brought 
out,  which,  like  all  high  speed  runners,  discharges  both  in  central 
and  outward  direction.  The  special  feature  of  this  Improved 
Samson  Wheel  is  the  partition  wall,  subdividing  the  runner  into 
two  sections.  The  upper  half  is  a  solid  casting,  the  lower  half 
has  steel  plate  buckets. 

Although  manufacturing  reasons  —  such  as  the  wish  to  use 
some  existing  patterns  or  pattern  parts  —  may  have  been  prevail- 
ing, it  is  more  than  doubtful  whether  the  addition  of  the  partition 
wall  is  an  advantage.  Without  going  any  further  into  this  mat- 
ter, only  a  few  reasons  for  this  opinion  of  the  writer  shall  be 
stated. 

The  partition  wall  increases  the  friction  loss  and  decreases  the 
effective  height  of  the  runner  and  thus  its  capacity.  Further,  it 
increases  the  possibility  of  clogging,  and  if  not  built  so  that  it 
coincides  with  the  corresponding  water  flow  lines,  it  will  decrease 
the  capacity  still  more. 

One  advantage  could  be  claimed,  namely,  that  the  regulation 
by  a  cylinder  gate  will  not  affect  the  efficiency  of  the  turbine  very 
much.  But  this  would  be  true  only  for  a  small  variation  of  load, 
when  the  cylinder  gate  closes  only  the  upper  part  of  the  runner. 


FIG.  15. 

IMPROVED  SAMSON  RUNNER. 


60  70 


FIG.  16. 
SPECIFIC  SPEED  AND  SPECIFIC  POWER  OF  THE  RUNNERS  MANUFACTURED  BY 

JAMES  IvEFFEl,  &  CO. 
IMPROVED   SAMSON   RUNNER. 


—   26   — 

TABLE  NO.  V. 

IMPROVED  SAMSON  RUNNER. 


Di 

Q* 

Jf-P, 

Ari 

Kv 

#, 

Kt 

K  V 

17 

671 

0.616 

92.8 

6.86 

3-34 

72-9 

o.86E 

20 

8.80 

0.808 

81.4 

7.10 

3-i6 

73-2 

0.886 

23 

11.63 

1.064 

70.8 

7.10 

3-17 

73-0 

0.886 

26 

14.87 

1.368 

62.6 

7.10 

3-17 

73-3 

0.886 

30 

19.79 

1.816 

54-2 

7.10 

3-17 

73-1 

0.886 

35 

26.83 

2.464 

46.4 

7.09 

3-15 

73-0 

0.885 

40 

35-19 

3-232 

40.6 

7.09 

3.  16 

73-1 

0.885 

45 

44-54 

4.088 

36.2 

7.10 

3-i6 

73-2 

0.886 

50 

"  54-99 

5.048 

32-4 

7-05 

3-i6 

72.9 

0.881 

56 

84.55 

6.328 

29.0 

7.08 

3-17 

73-2 

0.884 

62 

84.55 

7.760 

26.2 

7.09 

3-17 

73-i 

0.885 

68 

101.70 

9.336 

24.0 

7.11 

3-17 

73-3- 

0.887 

of  the  characteristic  constants  are 

Capacity  constant  K*  =  3.18. 
Speed  constant  Kv  =  7.07. 
Type  characteristic  #1  =  73.1. 

THE)  TRUMP   MFG.    CO.,    SPRINGFIEXD,   O. 

The  Trump  Mfg.  Co.  is  one  of  the  best  known  turbine  manu- 
facturers, mainly  on  the  foreign  market.  At  the  time  when 
European  concerns  were  not  willing  or  prepared  to  build  radial 


Fie.  17. 

TRUMP  RUNNER. 


20  30  40  .50  frO  70 


SPECIFIC  SPEED  AND  SPECIFIC  POWER  OF  THE  RUNNERS    MANUFACTURED  BY 
THE.  TRUMP    MANUFACTURING    CO. 

TRUMP  RUNNER. 


—   28   — 


inward  flow  turbines,  or  were  only  starting  to  do  so,  many  of 
.such  wheels  were  installed  by  -the  Trump  Mfg.  Co.  all  over  the 
European  continent.  Like  the  Samson,  the  Trump  runner  has 
steel  plate  buckets  and  in  form  resembles  the  other  American  high 
.speed  runners. 


TABLE  NO.  VI. 

TRUMP  RUNNER. 


£>i 

Qi  ' 

H-Pi 

Ni 

Kv 

#q 

K* 

Kf* 

14 

4.12 

0.375 

96.2 

5-89 

3.02 

58.9  . 

0.735 

17 

6.28 

0.570 

79-2 

5-89 

3-13 

59-8 

0.735 

20 

10.03 

0.801 

67.4 

5.89 

3-6l 

Co.  4 

0.735 

23 

I3-3I 

I.  210 

58.6 

5-87 

3-62 

64-5 

0.732 

26 

17.21 

1.564 

51-0 

5-78 

3-42 

63.7 

0.721 

30 

22.  6l 

2.135 

44-4 

5-8o 

3-62 

65.0 

0.723 

35 

30.86 

2.805 

38-2 

5-8o 

3-63 

64.1 

0.723 

40 

40.10 

3.646 

33-6 

5-88 

3-6l 

64.2 

0-734 

44 

48.51 

4.410 

30.6 

5.87 

3-62 

64-3 

0.732 

48 

57-70 

5.247 

28.0 

5.87 

3.61 

64.2 

0.732 

52 

63.43 

6.158 

25.8 

5-85 

3-37 

64.1 

0.730 

78.59 

7.136 

24.0 

5-87 

3-6l 

64.1 

0.732 

61 

92.92 

8-444 

22.  0 

5.87 

3-60 

64.0 

0.732 

66 

114.28 

10.384 

2O.4 

5-88 

3-77 

65-7 

0-734 

The  average  values  of  the  characteristic  runner  constants  are : 

Capacity  constant  K<i  —  3.52. 
Speed  constant  Kv  —  5.87. 
Type  characteristic  Kt  =  63.4. 


RISDON  ALCOTT  TURBINE  CO.,   MOUNT   HOLLY,   N.   J. 

The  types  of  runners  manufactured  by  the  Risdon  Alcott 
Turbine  Co.  are  very  numerous,  due  to  the  fact  that  this  concern 
is  a  combine  of  two  turbine  manufacturers,  the  T.  H.  Risdon  Co. 
and  the  T.  C.  Alcott  &  Son.  We  shall  consider  here  only  the 
Alcott  High  Duty  Special,  the  Risdon  Double  Capacity,  and  the 
Leviathan  runner. 


—  29  — 
TABLE  NO.  VII. 


AI,COTT 

HIGH    DUTY    SPECIAL 

RUNNER. 

0! 

H-Pi 

AT, 

K* 

K* 

Kt 

K'v 

1.65 

o.i55 

122.2 

5-28 

2.38 

48.2 

0.657 

2.26 

0.203 

100.8 

5-29 

2.26 

45-4 

0.66 

2.84 

0.257 

94.2 

5-35 

2.42 

47-7 

0.667 

3-52 

0.317 

83.4 

5-45 

2.25 

47.0 

0.68 

5-08 

0.456 

70.2 

5-52 

2.25 

47-4 

0.689 

6.90 

0.621 

59-8 

5-47 

2.25 

47.2 

0.682 

9.02 

0.812 

52.0 

5-45 

2.25 

46.8 

0.68 

11.36 

i  .027 

47.0 

5-52 

2.24 

47-7 

0.689- 

14.10 

1.269 

42.0 

5-49 

2.25 

47-3 

0.685 

20.31 

1.826 

35-2 

5-52 

2.26 

47.6 

0.689 

27.61 

2.483 

30.0 

5-50 

2.26 

47-3 

0.686 

36.09 

3.246 

26.2 

5-43 

2.25 

47-2 

0.684 

28.99 

2.727 

23-4 

5-50 

1-43 

38.7 

0.686 

35-94 
48.13 

3-258 
4-364 

21.0 
19.4 

5-50 
5.58 

1.44 
1-59 

37-9 
40-5 

0.686 
0.697 

FIG.  19. 
AIXOTT  HIGH  DUTY  SPECIAL  RUNNER. 


—  30  - 
TABLE  NO.  VIII. 

RIDSON  DOUBLE  CAPACITY  RUNNER. 


D* 

& 

H-Pt 

AT, 

K* 

K9 

K< 

K\ 

12 

1.17 

0.1064 

IOI.O 

5-29 

•  17 

33- 

0.66 

16 

2-34 

0.2256 

78-4 

5-50 

•  32 

37-2 

0.686 

20 

4.07 

0.3856 

66.0 

5-73 

•  50 

40.4 

0.715 

25 

6.78 

0.5104 

54-4 

5-95 

•54 

38.9 

0.742 

30 

II.  OO 

0.8024 

47.2 

6.12 

•76 

42.3 

0.764 

36 

15-60 

1.4032 

39-2 

6.15 

•73 

46.5 

0.707 

40 

18.93 

i  .  8240 

35-2 

6.18           ] 

•  7i 

47-5 

0.077 

43 

24-51 

2.3616 

33-0 

6.17           1 

.91 

50-7 

0.769 

50 

31.20 

2.8288 

26.8 

5-88           i 

.80 

45-1 

0-734 

54 

38-93 

3.536 

25.1 

5-89           ] 

.92 

47-2    • 

0-735 

60 

47-34 

4-5632 

22.4 

5.8o          ] 

•89 

47-8 

0.723 

66 

57.86 

5-5808 

21.6 

6.25           ] 

.91 

51-  1 

0.780 

72 

72.40 

6.5664 

28.8 

5.87          * 

5.01 

48.2 

0.732 

FIG.  20. 
RISDON  DOUBLE  CAPACITY  RUNNER. 


TABLE  NO.  IX. 

LEVIATHAN    RUNNER. 


Di 

& 

H-Fi 

ATi 

K* 

ft 

Kt 

K\ 

18 

6.67 

0.608 

95-0 

7-47 

2.96 

74- 

0.932 

21 

9.08 

0.824 

81.4 

7-45 

2.96 

74- 

0.930 

24 

11.86 

1.080 

71.2 

7-45 

2.96 

74.1 

0.930 

27 

15.01 

1.368 

63-4 

7-46 

2.96 

74-2 

0.931 

30 

18-53 

1.688 

57-0 

7-45 

2.96 

74.2 

0.930 

36 

26.68 

2.424 

47-6 

7-49 

2.96 

74-2 

0-935 

42 

36.32 

3-304 

40.8 

7.48 

2.96 

74-2 

0-934 

48 

47-43 

4.312 

35-6 

7-44 

2.97 

74- 

0.928 

54 

60.03 

5.456 

31-6 

7-44 

2.96 

73-9 

0.928 

60 

74.11 

6.736 

28.6 

7-47 

2.96 

74-3 

-0.932 

66 

89-67 

8.152 

26.0 

7-49 

2.96 

74-3 

0-935 

72 

106.72 

9.696 

23-8 

7-50 

2.96 

74-1 

0.936 

FIG.  21. 
LEVIATHAN  RUNNER. 


60  70 


FIG.  22. 


SPECIFIC  SPEED  AND  SPECIFIC  POWER  OF  THE  RUNNERS    MANUFACTURED  BY 
RISDON   ALCOTT   TURBINE   CO. 

A.  H.  D.  S. — ALCOTT  HIGH  DUTY  SPECIAL  RUNNER. 
R.  D.  C. — RISDON  DOUBLE  CAPACITY  RUNNER. 
L.— LEVIATHAN  RUNNER. 


—  33  — 

From  Table  No.  IX  it  appears  that,  similar  to  the  Improved 
New  American  runners,  the  nominal  diameters  are  larger  than 
the  real  mean  diameters.  The  values  of  the  speed  constant  Kv 
seem  to  be  too  large,  and  those  of  the  capacity  constant  too  small 
for  the  large  values  of  Kt. 

The  average  values  of  the  characteristic  runner  constants  are  : 

Alcott  High  Duty      Risdon 

Special      Double  Capacity  Leviathan 

Capacity  constant  K<i  ..............     2.25                    1.7  2.96  (?) 

Speed  constant  Kv  ................     5.46                    5.9  7-47  (?) 

Type  characteristic  Kt  ............  46.7                    43-8  74.1 

The  mean  values  of  the  Alcott  High  Duty  Special  have  been 
calculated  from  values  of  runner  diameters  up  to  48".  The  run- 
ners 54",  60"  and  66"  diameter  have  a  reduced  capacity. 

MORGAN  SMITH  CO.,  YORK,  PA. 

The  Morgan  Smith  Co.  manufactures  the  noted  McCormick 
and  New  Success  turbines.  Recently  a  new  type  has  been  put  on 
the  market  by  this  company  under  the  name  of  the  Smith  tur- 
bine. This  new  runner,  as  it  can  be  seen  from  Table  No.  XII, 
has  attained  somewhat  higher  values  for  Kt  than  those  of  the 
Improved  New  American,  which  was  the  leading  runner  in  this 
respect  until  the  Smith  Turbine  appeared. 

TABLE  NO.  X. 

MCCORMICK   RUNNER. 
A 

9 

12 

15 

18 

21 
24 
27 
30 


39 
42 

45 
48 
51 
54 

57 


0t 

H-Pi 

to 

Kv 

K* 

Kt 

K'r 

1.52 

0.138 

132.8 

5-22 

2.70 

49-2 

0.652 

2.65 

0.240 

99-6 

5-20 

2.45 

48.7 

0.649 

4.22 

0.382 

79-6 

5-20 

2.70 

49-2 

0.649 

6.17 

0.560 

64.4 

5.05 

2.74 

48.2 

0.630 

8-73 

0.792 

61.2 

5.61 

2.85 

54-5 

O.70O 

11-53 

1.046 

50.6 

5.30 

2.88 

51-8 

0.661 

14.61 

1.308 

47-2 

5-55 

2.88 

54-0 

0.630 

17-59 

1-595 

41.6 

5-44 

2.82 

52.6 

0.680 

21-53 

I-95I 

36.2 

5-20 

2.85 

50.6 

0.652 

24.71 

2.240 

35-4 

5-55 

2.75 

53-0 

0.693 

29.05 

2.634 

31-0 

5-28 

2-75 

50.2 

0.657 

35.67 

3-233 

30.0 

5-49 

2.92 

54-0 

0.687 

37.98 

3-444 

27-4 

5-37 

2.70 

50.8 

O.67O 

42.85 

3-885 

24.6 

5-14 

2.78 

48.5 

0.694 

48.79 

4-433 

24.8 

5-51 

2.69 

52.2 

0.687 

57-44 

5-208 

22.8 

5.38 

2.84 

52.1 

O.67I 

64.45 

5.843 

22.2 

5-51 

2.86 

53-7 

0.688 

FIG.  23. 

MCCORMICK  AND  NEW   SUCCESS  RUNNER. 


FIG.  24. 


—  35  — 
TABLE  NO.  XI. 

NEW   SUCCESS  RUNNER. 


A 

a 

H-P, 

Ni 

K? 

K* 

Kt 

K\ 

9 

1.47 

0.133 

146. 

5-72 

2.62 

53-1 

0.713 

12 

2-57 

0.233 

109.4 

5-72 

2.57 

52-7 

0.713 

15 

4-C9 

0.370 

87.4 

5-72 

2.62 

53-2 

0.713 

18 

5-99 

0-543 

70.8 

5-55 

2.66 

52.2 

0.693 

21 

8:47 

0.768 

67.2 

6.17 

2.76 

58.8 

0.770 

24 

11.19 

1.014 

55-6 

5-8i 

2.80 

55-9 

0.724 

27 

14.17 

1.284 

51-8 

6.  10 

2.79 

58.8 

0.761 

30 

17.06 

1-547 

45-6 

5.96 

2-73 

56.7 

0.744 

33 

22.74 

1.898 

39-8 

5-72 

3.00 

54-9 

0.713 

36 

23-97 

2.173 

38.8 

6.07 

2.64 

59-2 

0.758 

39 

28.18 

2-554 

34-0 

5.78 

2.87 

54-3 

0.721 

42 

34.60 

3-136 

33-0 

6.04 

2.83 

58.4 

0-754 

45 

36.84 

30.0 

5-88 

2.61 

54-7 

0-734 

48 

41-57 

3.768 

28.6 

5-98 

2.64 

55-6 

0.746 

5i 

47.29 

4.290 

27.2 

6.05 

2.61 

56.4 

0-755 

54 

55-12 

5-051 

25.0 

5.88 

2.75 

56.2 

0-734 

57 

62.51 

5.667 

24.4 

6.07 

2.77 

58.1 

0-757 

60 

81.03 

7-340 

22.6 

5-90 

3-24 

61.3 

0.736 

66 

98.04 

8.888 

20.4 

5-88 

3-23 

60.8 

0.734 

72 

123.37 

11.187 

18.6 

5.83 

3-42 

62.2 

0.728 

84 

167.99 

14.430 

16.0 

5-86 

3-42 

60.8 

*  0.931 

TABLE 

NO  XII. 

SMITH 

RUNNER. 

A 

'        0i 

H-Pi 

AT, 

Kv 

Kn 

Kt 

K'* 

12 

3-68 

0.338 

138.6 

7.28 

3-73 

80.5 

0.910 

15 

5-8i 

0.530 

no.  8 

7-26 

3-73 

80.7 

0.907 

18 

8.28 

0.760 

92.4 

7-23 

3-67 

80.5 

0.903 

21 

1  1  .29 

1.034 

79-2 

7-25 

3-69 

80.5 

0.905 

24 

14-73 

1-353 

69.2 

7-25 

3-67 

80.5 

0.905 

27 

18.63 

1.710 

61.6 

7-25 

3-68 

80.7 

0.905 

30 

23.01 

2.113 

55-4 

7-25 

3-68 

80.5 

0.905 

33 

27-85 

2.558 

50.6 

7-30 

3-68 

80.9 

0.912 

36 

33-19 

3-047 

40-4 

7.29 

3-68' 

81.0 

0.911 

39 

42 

38.91 

45.10 

3-573 
4.143 

42.6 
39-6 

7-25 
7.26 

3-69 
3-69 

80.5 
80.5 

0.905 
0.906 

45 

51.76 

4-753 

37-o 

7-25 

3-67 

80.8 

0.905 

48 

58.43 

5.362 

34-6 

7-25 

3-65 

80.2 

0.005 

51 

66.56 

6.  in 

32-6 

7-26 

3-68 

80.7 

0.906 

54 

74.90 

6.850 

30.8 

7.28 

3-69 

80.7 

0.910 

57 

83.12 

7.632 

29.2 

7.26 

3-70 

80.7 

0.906 

60 

92.10 

8.456 

27.8 

7-30 

3-68 

80.7 

0.912 

63 

101.56 

9-324 

26.4 

7-25 

3-67 

80.7 

0.905 

66 

111.45 

10.233 

25.2 

7.28 

3-67 

80.7 

0.910 

72 

132-64 

12.178 

23.0 

7.22 

3-68 

80.3 

0.902 

-36- 

The  average  values  of  the  characteristic  runners  are : 

McCormick  New  Success        Smith 

Capacity  constant  tf, 2.96 

Speed  constant  Kv 5-35  5-88 

Type  characteristic  Kt Si-4  55- 

THE  WELLMAN-SEAVER-MORGAN   COMPANY,   CLEVELAND,  OHIO. 

The  "Standard"  runner  manufactured  by  the  Wellman-Sea- 
ver-Morgan  Co.  is  the  Jolly  McCormick  runner.  A  table  of  the 
characteristics  and  curves  of  this  runner  has  been  omitted,  as  they 
are  exactly  the  same  as  those  of  the  McCormick  runner,  manu- 
factured by  the  S.  Morgan  Smith  Co.  See  Table  No.  X,  and 
curves,  Fig.  25. 

The  Wellman-Seaver-Morgan  Co.  manuafctures  also  a  "Spe- 
cial" runner  with  increased  capacity  and  increased  speed.  Judg- 
ing from  the  test  of  a  33"  turbine,  the  values  of  the  character- 
istic runner  constants  are : 

Capacity  constant  Kd  =  3.2. 
Speed  constant  Kv  =  6.49. 
Type  characteristics  Kt  =  68.2. 

Lately  this  company  produced  another  remarkable  runner 
with  the  following  characteristic  constants : 

Capacity  constant  7£q  =  3.6  (3.96). 
Speed  constant  Kv  =  6.47. 
Type  characteristics  Kt  —  78.5- 

whereby  the  value  Kq  =  ^.6  corresponds  to  So%  efficiency,  which 
value  was  assumed  as  basis  for  all  other  runners.  The  value 
^  =  3.96,  corresponds  to  the  actual  discharge  Q±  =  2i  and 
actual  best  efficiency  86%. 

Arranging  now  the  various  runner  types  according  to  their 
type  characteristics,  we  will  have  answered  the  question,  how  far 
the  different  concerns  have  come  in  reference  to  the  aim  of  high- 
est capacity  and  highest  speed  with  good  efficiency.  Table  No. 
XIII  gives  both  the  mean  and  the  maximum  values  of  Kt  which 
were  reached  by  the  various  runners  and  the  corresponding  ca- 
pacity and  speed  constants  Kq  and  Kv. 

As  European  engineers  and  European  text  books  frequently 
refer  to  the  American  high  speed  runners,  and  as  it  appears  that 
the  information  they  have  regarding  the  same  is  very  inaccurate, 


10      .        20  30  4-0  50  60  /Q 

FIG  25. 

SPECIFIC  SPEED  AND  SPECIFIC  POWER  OF  THE  RUNNERS   MANUFACTURED  BY 
S.   MORGAN   SMITH   CO. 

M.   C. — MCCORMICK  RUNNER. 
N.   S. — NEW  SUCCESS  RUNNER. 
S. — SMITH   RUNNER. 


--I 


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—  39  — 


the  runner  characteristics  have  been  given  also  in  the  metric 
system. 

For  i  (ft.)  =0.30479  (m),  i  (cub.  ft.)  =0.028317  (cub.  m.), 
i  (H-P)  =  1.01385  (cheval  vapeur)  =  1.01385  (metric  H-P). 

The  following  conversion  constants  are  to  be  used,  when  con- 
verting from  the  foot  system  into  the  metric  system. 

a" 

PN 


—  40  — 

EXAMPLE: — 36"  Smith  runner;  see  Table  XII. 
Foot  system.  Metric  system. 

Q!         =33.19  0.05I3X33.I9     =        L703 

Ni      =46.4  1/0.552    X46-4     =   84.1 
H-P1=   3-047      6. 0246  X    3-047=    18.1 
K«     =   3.68       0.552   X    3-68   =     2.032 
K?     =   7.29       0.552   X   7-29   =     4-025 
Kt      =81.0         4-447    X8i.       =360. 


FIG.  26. 
JOIAY  MC  CORMICK  RUNNER. 


—  41  — 

For  clearness  two  sets  of  curves  have  been  drawn,  showing 
the  specific  power  and  speed  of  the  various  runner  types.  In 
Fig.  27  the  curves  of  the  Improved  Samson  and  Trump  runner 
have  been  omitted,  as  they  would  interfere  with  those  of  other 
runners. 

The  curve  of  the  Improved  Samson  runner,  as  can  be  seen 
from  the  values  of  Kq  in  Table  V,  would  almost  coincide  with 
that  of  the  Victor  Standard  Capacity  runner.  The  curve  of  the 
Trump  runner  with  that  of  the  Victor  Increased  Capacity.  The 
curve  of  the  Leviathan  runner  has  been  drawn  as  dotted  line, 
because  the  nominal  diameters  of  this  runner  type  s.eem  to  be 
larger  than  the  real  mean  diameters  and  a  correction,  like  with 
the  Improved  New  American,  could  not  be  made  for  lack  of  in- 
formation. Judging  from  the  value  of  Kt  the  curve  should  be 
in  neighborhood  of  those  for  the  Smith  and  Improved  New  Amer- 
ican runners. 

For  the  same  reasons,  the  speed  curves  of  the  Leviathan,  Im- 
proved Samson  and  Trump  runners  have  been  omitted  in  Fig. 
No.  28. 

ABBREVIATIONS. 

S  =  Smith. 

I.  N.  A.  =  Improved  New  American. 

L,.  —  Leviathan. 

V.  I.  C.  —  Victor  Increased  Capacity. 

V.  S.  C.  =  Victor  Standard  Capacity. 

N.  b.  =  New  Success. 

N.  A.  =:  New  American. 

M.  C.  =  McCormick. 

A.  H.  D.  S.  =  Alcott  High  Duty  Special. 

R.  D.  C.  =  Risdon  Double  Capacity. 

At  the  end  it  may  be  emphasized  that  it  was  not  the  intention 
of  the  writer  to  decide  which  runner  type  is  best.  To  endeavor 
to  answer  such  a  question  would  be  absolutely  wrong.  There  can 
not  be  a  runner  which  would  be  best  for  all  conditions.  In  many 
cases  the  best  efficiency  will  be  the  deciding  factor,  but  very  fre- 
quently the  variation  of  the  efficiency  with  the  variation  of  load, 
and  sometimes  the  maximum  capacity  or  the  maximum  speed  wilj 


FIG.  27. 
SPECIFIC  POWER  OF  THE  AMERICAN  STANDARD  HIGH  SPEED  RUNNERS. 


—  43  — 

determine  which  is  the  best  runner  for  a  given  case.  Not  seldom, 
for  merely  technical  reasons,  the  best  runner  may  be  one  which 
for  capacity,  speed  and  efficiency  occupies  a  minor  position  among 
the  other  runners. 


10  2O  30  4O  50 


FIG.  28. 
SPECIFIC  SPEED  01-  THE  AMERICAN  STANDARD  HIGH  SPEED  RUNNERS. 


—  44  — 

AUJS-CHAI/MERS  CO.,  MILWAUKEE,  WIS. 

The  manufacture  of  hydraulic  turbines  was  begun  by  the 
Allis-Chalmers  Company  only  six  years  ago.  Following  in  the 
beginning  the  European  principle,  turbines  were  designed  to  suit 
given  conditions  and  requirements  in  every  instance.  But  the 
advantage  of  standard  turbines  being  fully  appreciated,  long  and 
exhaustive  studies  have  been  made  in  this  direcion  by  the  com- 
pany's engineers. 

At  the  present  time,  the  developing  work  on  Allis-Chalmers 
standard  turbine  types  is  practically  completed.  In  order  that 
all  ordinary  combinations  of  speed  and  capacity  may  be  covered 
by  these  "standards,"  the  company  is  building  six  different  types 
of  radial  inward-flow  runners  for  Kt=  13  to  about  80,  and  two 
types  of  impulse-wheel  buckets.  Here  only  the  high  speed  run- 
ner, Type  F,  interests  us.  This  type  was  designed  to  have  at 
least  a  type  characeristic  Kt=  68.  The  first  runner  of  this  type, 
a  3O-in.  runner,  was  tested  in  the  Holyoke  testing  flume  after  the 
first  publication  of  this  article  in  the  summer  of  1909.  The  result 
of  this  test,  although  within  the  expectations  of  the  engineers, 
was  far  beyond  the  anticipations  of  the  company.  The  following 
data  obtained  from  the  test  are  interesting. 

At  best  efficiency,  82.5%,  the  turbine  developed  power  at  the 
rate  H-Pl=  2.28  with  a  speed  Nj==  52.  Thus  the  values  of  the 
runner  constants  are  : 


Allis-Chalmers  "Type  F." 


=  3.89 
=  6.8 


With  increased  speed,  the  efficiency  went  down  very  slowly, 
but  the  output  was  increased.  At  speed  proportional  to  N1=  59, 
the  power  was  proportional  to  H-P^=  2.34.  Thus 


=  3.80 
=   7-72 


SECOND  SECTION 


A  RATIONAL  METHOD  OF  DETERMINING  THE  PRIN- 
CIPLE DIMENSIONS  OF  WATER-TURBINE 
RUNNERS. 


S.    J.    ZOWSKI,    ASSISTANT    PROFESSOR    OF    MECHANICAL 
ENGINEERING. 


[Copyrighted,  1909,  by  S.  J.  Zowski.] 

The  principal  dimensions  of  a  water  turbine  runner  are  deter- 
mined from  the  required  speed  and  capacity  and  the  available 
head  of  water. 

Let  D  =  the  mean  runner  diameter,  in  feet. 

v  =  the  corresponding  peripheral  speed,  in  feet  per  second. 

N  =  the  required  rotative  speed,  in  revolutions  per  minute, 
then  v  —  irDN/6o  and  D  =  6oz/AN   (i ) 

so  that  when  the  proper  peripheral  speed  to  give  good  hydraulic 
performance  is  known  the  diameter  of  the  runner  follows  there- 
from. 

Let  us  assume  that  the  runner  is  designed  in  such  a  wray  that 
at  its  best  speed  the  water  discharges  from  the  runner  buckets 
in  planes  going  through  the  axis  of  rotation;  this  is  a  condition 
which  the  turbine  designer  should  always  attempt  to  secure,  in 
order  to  avoid  helical  stream  lines  in  the  draft-tube.  Then  the 
best  peripheral  speed  is  given  by  a  simple  formula.  Denoting 
the  bucket  angle  by  /?,  the  guide-vane  angle  by  a,  as  in  Fig.  i ,  and 
the  hydraulic  efficiency  by  en,  the  formula  is : 


^x,- 

where 


K,  =  y 


The  curves  in  Fig.  2  give  the  values  of  the  second  radical  for 
several  constant  values  of  bucket  angle  ft  with  varying  values  of 

*  Reprint    from    Engineering    News.      Cuts    loaned    by    courtesy  of 
I'.nginecring  News. 


guide  vane  angle  a.     The  following  limits  for  a  and  (3  appear 
reasonable. 


FIG     j — SECTION  THROUGH   RADIAL  INWARD-FLOW  TURBINE  SHOWING  RELATION 
BETWEEN   BUCKET  AND   GUIDE-VANE   ANGLES. 

For  a  pronounced  low-speed  turbine  /3  =  6o°.  a  =  20°;  then 


\  sin  (ft -a] 
\  sin  ft  cos  a  = 

For  a  pronounced  high-speed  turbine  /3=  135°,  a  =  40°  ;  then 


|  sin  (ft  —  a) 
\|  sin  /?  cos  a  ~ 

For  simplicity  we  will  assume  that  medium-speed  runners 
(/?  — 90°)  show  a  hydraulic  efficiency  of  84%  (giving 
Vehg  ==5.198),  and  other  types  of  runner  an  efficiency  of  83% 
(giving  Vehg  =5.167).  These  values  are  by  no  means  taken 
too  high  for  runners  of  fair  design  and  construction.  .  Then  the 
speed  constant  has  for  the  different  types  the  following  values : 


Type  of  Runner 

Low-speed    ()3  =  60°  to  90° ) 
Medium-speed  (P  =  go°) 
High-speed   (/3  =  90°  to  135°) 


Speed  Constant  Kv 
4.588  to  5-198] 
5.198  (4) 

5.198  to  7.006  J 


16 

EN6.NEWS. 


Z4- 


28 
in         Degrees. 

FIG>    2.. — CURVES    FOR   FINDING   THE    NORMAL    PERIPHERAL    SPEED   OF    A   TURBINE 
RUNNER    FOR    GIVEN     BUCKET    AND    GUIDE-VANE    ANGLES. 

The  ordinates  give  values  of 


i'  sin  (ft  — a) 
\|  sin  ft  cos  (i 


The  speed-constant  is 


X 


sin  (ft—  a) 


where  ^  =  hydraulic  efficiency;  9  =  gravity  constant. 

The    desired    peripheral    speed    of    the    wheel    in    feet    per 
second    is 

z>  =  A'v  i/  If 
where  //  =  effective  hydraulic  head  in  feet. 


For  very  high  heads,  which  naturally  will  require  low-speed 
runners,  it  will  be  wise  not  to  approach  the  minimum  value  of  /?, 
but  to  remain  in  the  neighborhood  of  90°,  for  the  following 
reason:  The  smaller  the  angle  /?,  or  to  be  more  exact,  the 
smaller  the  ratio  /?/«,  the  smaller  is  the  pressure-head  under 
which  the  water  passes  from  the  guide  case  into  the  runner 
buckets.  This  reduced  pressure  will  facilitate  the  separation  of 
the  air  that  is  contained  in  the  water,  and  thus  it  will  facilitate 
honey-combing  of  the  runner  and  guide  case,  so  often  observed 
^ven  in  turbines  otherwise  most  carefully  designed  and  highly 
finished. 

Substituting  the  values  of  Kv  in  eq.  ( i )  we  obtain  the  follow- 
ing simple  formulas  for  the  runner  diameters : 

Type  of  Runner  Formula  for  Diameter 


Low-Speed  X  V~H 

Medium-Speed  9       x  ]  /~H 


High-Speed  X   V~H 


7 

(5) 


As  far  as  speed  alone  is  concerned,  any  diameter  within  the 
above  wide  limits  could  be  used.    The  required  capacity,  however, 
will  limit  the  choice  considerably.     The  following  considerations 
deal  with  the  influence  of  capacity. 
Let  n  =  number  of  buckets. 

n'  =  number  of  guide  vanes. 
/   =  thickness  of  bucket  edge. 

/'    =  width  of  the  eddy  caused  by  the  guide  vane  tips  and 
measured  on  the  runner  circumference  (see  Fig.  3). 
Then  the  actual  entrance  area  is  : 


where 

.,  n  t  ri  t' 


and 


(8) 


As  to  the  number  of  buckets  used  differences  of  practice  will 
be  found  among  turbine  builders.     While  a  few  of  them  use  in 


FlG.   3. — SECTION  THROUGH   GUIDE-VANE  AND  BUCKET  TIP. 

every  case  as  large  a  number  of  buckets  as  possible,  the  majority 
put  into  a  high-speed  runner  fewer  buckets  than  into  a  low-speed 
runner.  The  following  empirical  formulas,  in  which  D  is  ex- 
pressed in  inches,  will  give  satisfactory  results. 

<«  ,  „  Approx.  Number 

Type  of  Runner  ^of  Buckets 

Low-Speed  n  =  3.7  }/  D 

Medium-Speed  n  =  3.0  ]/'  D  (9) 

High-Speed  n  =  2.2  j /  D 

The  number  of  guide-vanes  is  very  often  determined  by  the 
simple  rule  that  in  every  case  a  few  more  guide-vanes  than  buck- 
ets should  be  put  in  (i.  e.,  n'  =  i.i  n  to  1.3  n).  This  rule,  how- 
ever, gives  low-speed  runners  too  many  guide-vanes,  thereby 
(on  account  of  the  small  angles  a  which  are  used  in  low-speed 
turbines)  the  gate  openings  become  too  small  and  correspondingly 
the  frictional  surfaces  become  relatively  large.  Therefore  it  is 
proper  to  take  account  of  the  guide-vane  angle  in  choosing  the 
number  of  vanes.  The  following  empirical  formulas  will  give 
good  results.  Again  taking  D  in  inches, 

Approx.  Number  of 
Guide-vane  angle  a  Guide-vanes 


20°  and  less  n'  =  2.5  y  D 

20°  to  30°  ,,'=3.o|/77 

30°  to  40°  n'  =  3.5  I/  D  \ 


-_  6  — 

Since  for  manufacturing  reasons  it  is  advisable  that  the  num- 
ber of  guide-vanes  be  even,  and  possibly  divisible  by  four,  it  will 
be  best  to  use  an  even  number  of  buckets,  in  order  to  avoid  hav- 
ing more  than  one  bucket  edge  coincide  with  a  guide-vane  tip  at 
the  same  time.  On  this  basis  the  curves  in  Fig.  4  have  beer* 
drawn.  These  may  be  used  instead  of  eq.  (9)  and  (10). 


OH- 

28 
20 
12 

35 
31 
27 
23 

>» 
15 
11 

7 

*=30 

\fo40 

0 

Num 

ber  a 

f  6uia 

?-Vcrn 

es 

a=SO 

A&~* 

w°eci 

o  - 

ess 

I 

\ 

i 

\ 

J 

1 

___ 

i- 

r  —  - 
i 

J 

J 

/3-& 

0vfc9, 

r<7^ 

\ 

Num 

ber  o 

f    Bu 

ckei-3 

r™ 

./&- 

<30° 

\ 

1 

r 

r 

j 

\ 

\ 

J3- 

*30°to  i 

35° 

1 

1 

r 

r 

\  . 

1 

\ 

\ 

r 

1 

_J 

R        18  «    24       250       36       42       48        54      60        66       72       78       84 
(  KNQ.  NEWS.  _  >  Diame-Ver      of       "Runner       in       Inches. 

FlG.   4.— DIAGRAM    GIVING    NUMBER   OF   BUCKETS    AND    NUMBER   OF   GUIDE-VANES. 
FOR    DIFFERENT    TYPES    AND    SIZES    OF    RUNNERS. 

The  eddies  caused  by  the  guide-vane  tips  should  be  reduced 
to  a  minimum.  The  writer  advises  strongly  to  design  the  guide 
case  in  such  a  way  as  to  get  point  x  (see  Fig.  3)  outside  of  the 
runner  circumference.  This  obviously  must  be  obtained  by  shap- 
ing the  vane  tips  properly  and  by  leaving  a  sufficient  clearance 
between  vane  and  bucket  tips.  If  this  is  done  the  entering 
streams  of  water  will  join  in  a  solid  ring,  and  the  effect  of  the 


eddies   on   the   capacity   of    the   runner   will   be   nullified.      The 
constant  K±  will  then  have  the  value. 


The  thickness  t  varies  between  %-in.  and  ,T4-in.  for  steel 
plate  buckets,  and  between  %-in.  and  %-in.  for  cast  buckets. 

The  following  gives  the  values  of  K±  for  three  different 
runner  sizes,  computed  from  eq.  (  1  1  )  : 


*  —  Constant  K!—  -> 

tf^  m  *       ^ja  Steel  plate  buckets  Cast  buckets 

£>  j8         » 

60°       13  O.QI54 

i  ft.        90°       ii  f.=  }^  in.  0.9635  t  =  Y4\n.  0.9270 

135°  0.9671  0.9542 

60°  25  0.9600 

4  ft.    90°  21  t  =  1A  in.     0.9652  f  =  54  in.     0.9652 

135°  15  0.9649  0.9298 

60°  33.  0.9557 

7  ft.  90°  27  t  —  Y4  in.  0.9744  t  =  •}«  in.  0.9616 

135°  19  0.9745  0.9618 

For  simplicity  we  shall  assume  that  K1  has  the  uniform  value 
0.93  for  all  runner  types  and  sizes,  with  the  distinct  understand- 
ing however  that  in  the  final  computation  the  exact  value  is  to  be 
introduced,  and  also,  if  necessary,  the  item  n'  t'  be  considered. 

The  capacity  of  the  turbine  depends  very  directly  on  the 
ratio  B/D,  or  K2.  As  a  matter  of  fact  it  is  this  ratio  which  finally 
determines  the  limits  for  the  application  of  radial  inward-flow 
turbines.  Turbine  manufacturers  are  still  struggling  with  the 
problem  of  extending  these  limits  in  both  directions  ;  therefore 
no  definite  maximum  or  minimum  values  can  be  given. 

Present-day  good  practice  indicates  that  until  further  advance 
is  made  it  is  safe  to  fix  the  limits  of  breadth  of  runner  at  1/30 
and  l/2  the  diameter.  The  minimum  value  depends  on  the  purity 
of  the  water.  The  maximum  value  which  could  be  allowed  de- 
pends on  the  design  of  the  runner,  for  it  is  evident  that  the  larger 
the  width  of  the  runner,  the  more  difficult  it  is  to  secure  the 
necessary  passage  area  at  the  point  where  the  water  turns  from 


—  8  — 

radial  to  axial  direction.  In  the  opinion  of  the  writer  it  is  pos- 
sible to  go  somewhat  above  l/2  with  the  ratio  of  width  to  diam- 
eter, but  then  the  runner  must  be  bulged  out  sufficiently. 

We  have  classified  all  runners  under  three  types  with  refer- 
ence to  speed.  It  is  customary  to  make  a  further  classification; 
with  reference  to  capacity.  Here  also  we  distinguish  three  types. 
The  latter  classification  is  based  on  the  proportions  of  the  runner 
profile,  or  the  ratios  of  ( i )  diameter  at  entrance  point  of  buckets, 
(2)  diameter  at  exit  point  of  bucket,  (3)  diameter  of  neck  of 
draft-tube.  These  diameters  (Fig.  5)  will  be  denoted  by  D,  D', 
and  D" '.  Their  ratios  depend  mainly  on  the  factor  Kz,  or  B/D. 

Type  L,  or  the  low-capacity  type,  comprises  all  runners  in 
which  the  draft-tube  diameter  D"  is  less  than  the  bucket  exit 
diameter  D' ',  or  at  most  equal  to  it,  and  in  which  B/D  lies  be- 
tween 1/30  and  y%.  Type  II.,  the  medium-capacity  type,  com- 
prises runners  in  which  D"  is  larger  than  D'  but  smaller  than  the 
entrance  diameter  D,  and  in  which  B/D  lies  between  y%  and  y\. 
Type  III.,  or  the  high-capacity  type,  comprises  all  runners  in 
which  the  draft-tube  diameter  D"  exceeds  the  bucket  entrance 
diameter  D,  and  in  which  B/D  is  between  y+  and  l/2, 

It  is  self-evident  that  high  heads  will  require  runners  of  both 
low-capacity  .and  low-speed  type,  while  low  heads  will  call  for 
high-capacity  high-speed  runners.  In  other  words,  small  values 
of  K2  naturally  go  with  small  values  of  Kv,  and  large  values  of 
K2  go  with  large  values  of  Kv.  Mistakes  in  this  respect  are  fre- 
quently made  by  manufacturers  of  low-head  turbines,  when  they 
occasionally  build  a  high-head  turbine,  by  giving  the  runner  buck- 
ets of  such  turbines  the  same  entrance  angles  (/?>9o°)  as  are 
used  on  their  low-head  turbines.  This  increases  the  peripheral 
speed  so  much  that  the  runner  diameter,  and  consequently  the 
size  of  the  whole  turbine,  must  be  increased  considerably  in  order 
to  obtain  the  required  rotative  speed. 

A  runner  is  characterized  as  to  its  capacity  by  the  so-called 
capacity  constant, 


(12) 

V HD* 


—    IO   — 


The  values  of  Kq  for  the  different  runner  types  can  be  found 
as  follows :    Area  X  Speed  =  Discharge ;  therefore, 

Q  =  -n-K1K2D-cf  (13) 

where   cr   is   the   radial   component   of    the   entrance   velocity   c 
(see  Fig.  i).     This  component  is  given  by 


Cr  =  c  sin  a  =i/  eh  gsin(-a}cosa   sin  a  =  **        H        (J4) 

Combining  the  last  two  equations,  we  get 

Q  =  -  K\  Kz  A'8  1/77  D*  =  A*q  1/77"  D*  (15) 

or, 

K*  =  irK1K2K3  (16) 

in  which 


sin  ft 
Sin(l3-a)cosa    sin  a 


In  Fig.  6  is  drawn  a  series  of  curves  which  give  the  values 
of  the  second  radical  of  eq.  (17)  for  the  same  angles  ft  and  a  for 
which  the  curves  in  Fig.  2  were  drawn.  Multiplying  the  appro- 
priate ordinate  taken  from  Fig.  6  by  V^iTJ,  we  obtain  K3.  The 
other  coefficients  (K±  and  K2)  having  been  found  previously, 
eq.  (16)  at  once  gives  the  value  of  the  Capacity  Constant  Kq. 

Using  the  same  limiting  values  as  before,  to  define  the  several 
types  of  runner,  we  find  that  the  Capacity  Constant  has  the 
following  range  : 

Type  of  runner  Range  of  K* 

Low-speed  low-capacity  0.21  to  0.89] 

Medium-speed   medium-capacity  0.89  to  2.19  \     (18) 

High-speed  high-capacity  2.19  to  4.66] 


—  II  — 


0.7 


0.6 


- 


^    0.4 
1 
0.3 

0.2 


#%xx 


/ 


y 


X  * 


x 


X 


x 


wor5 


••••/£0° 


/ 


16 


20 


24  28  32 

cc        in         Degrees. 


36 


40 


i    6, — CURVES    FOR    FINDING    RADIAL   ENTRANCE   VELOCITY    FO.*    GIVEN    BUCKET 
AND   GUIDE-VANE   ANGLES. 


The  ordinates  give  values  of 


a)  COS  a 


The  factor 


i"3  =  I/  e\\  g  •    ^\ 


sin  (ft  —  a)  cos  a 


sin  a 


where  ^  =  hydraulic  efficiency  ;  g  =  gravity  constant. 
The  radial  entrance  velocity  in  feet  per  second  is 


where  H  =  effective  hydraulic  head  in  feet. 


—    12   — 

By  introducing  these  values  in  eq.  (12)  and  solving  for  diameter 
we  obtain  the  following  simple  formulas: 

Diam.  in  terms  of  discharge 

Type   of   runner  per    i-ft.    head 

Low-speed  low-capacity  (2.20  to  1.06)    \/~0i  ) 

Medium-speed   medium-capacity  (1.06  to  0.67)    ^/~Q[   >-    (19) 

High-speed    high-capacity  (0.67  to  0.46)    -\J~Q[  ) 

These  formulas,  together  with  eq.  (5),  will  determine  which 
range  of  diameters  can  satisfy  both  the  requirements  as  to  speed 
and  capacity.  Evidently  only  those  diameters  are  suitable  which 
satisfy  both  eq.  (5)  and  eq.  (19). 

The  procedure  can  be  further  simplified  by  the  use  of  a  con- 
stant which  the  writer  has  called  Type  Characteristic  (see  Eng. 
News,  Jan.  28,  1909).  Its  formula  is: 

N  X  V  H-P       60  Jvv  X  |/5q  X  V~K 

Kt  = — —  = (20) 

H  i^H  TT 

where 

H-P       62.42  X  turbine  efficiency 

~  QH  550 

For  a  turbine  efficiency  of  80%,  K==i/n,  which  may  be 
used  as  a  fair  average  value  for  the  present  purpose.  With  this 
figure,  and  the  values  of  K^  and  'Kv,  tabulated  previously,  we 
obtain  the  following  ranges  for  the  Type  Characteristic : 

Type  of  runner  Type  characteristic  7vt 

Low-speed  low-capacity  12  to  28    ] 

Medium-speed    medium-capacity  28  to  44    }•       (21) 

High-speed  high-capacity  44  to  87    J 

With  these  formulas  the  determination  of  proper  runner  type 
and  diameter  is  very  simple.  We  proceed  as  follows : 

From  the  given  values  of  horsepower  output  H-P,  speed  of 
revolution  A7,  and  hydraulic  head  H,  compute  the  type  character- 
istic Kt  by  eq.  (20).  If  the  resulting  figure  is  between  12  and  28, 
a  radial  inward-flow  turbine  is  possible,  and  the  runners  will  have 
to  be  of  the  low-speed,  low-capacity  type,  with  B/D  =  1/30  to  J/6, 


/?=:6o0  to  90°,  and  a  profile  which  will  fall  between  profiles 
A  and  B  of  Fig.  5. 

If  the  value  of  Kt  is  between  28  and  44,  the  runner  will  have 
to  be  of  the  medium-speed,  medium-capacity  type,  with  B/D  = 
Y&  to  ^4,  /?  =  9o°,  and  a  profile  which  will  fall  between  profiles 
B  and  C  of  Fig.  5. 

If  the  value  of  Kt  is  between  44  and  87,  the  runner  will  have 
to  be  of  the  high-speed,  high-capacity  type,  with  B/D  =  %  to  J/>. 
/3  =  9O°  to  135°,  and  a  profile  which  will  fall  between  profiles 
C  and  D  of  Fig.  5. 

If  the  value  of  Kt  is  smaller  than  12,  and  it  does  not  seem 
advisable  to  make  B  smaller  than  1/30  of  the  diameter,  a  radial 
inward-flow  turbine  is  not  possible,  and  an  impulse  wheel  will 
have  to  be  used. 

If  the  value  of  Kt  is  larger  than  87,  a  multiplex  turbine  must 
be  built.  That  is  to  say,  a  case  for  which  Kt  is  found  to  be,  say, 
174,  which  is  2  X  87,  would  require  a  quadruplex  turbine  of 
which  each  runner  is  designed  for  Kt  =  87. 

Knowing  the  type  of  runner  it  is  easy  to  find  the  other  prin- 
cipal dimensions,  as  now  we  can  not  make  a  mistake  in  the  choice 
of  the  rational  values  for  the  different  constants  in  our  equa- 
tions. A  few  words  must  be  added,  however,  in  reference  to  the 
draft-tube  diameter  D".  The  flow  velocity  c"  at  the  point  where 
D"  is  measured,  the  "upper  draft-tube  area,"  is,  in  properly 
designed  runners,  more  or  less  the  same  as  the  flow  velocity 
in  the  discharge  area  of  the  runner.  This  velocity  represents  a 
direct  loss;  but  the  loss  is  partly  recovered  by  the  conical  lower 
part  of  the  draft-tube.  In  low-capacity  runners  there  is  no  diffi- 
culty in  reducing  the  discharge  loss  to  a  minimum  in  the  runner 
itself.  In  high  capacity  runners,  on  the  other  hand,  larger  dis- 
charge losses  must  be  allowed,  as  otherwise  the  runner  would 
have  to  be  bulged  out  too  much.  Expressing  the  discharge-  loss 
measured  at  the  upper  draft-tube  area  in  parts  of  the  total  head, 
the  following  values  will  represent  good  practice. 


Type    of    runner 
Low-speed  low-capacity 
Medium-speed    medium-capacity 
High-speed  high-capacity 


Discharge  Joss  in  terms 

of  total  head 
(0.04  to  0.06)  H         ] 
(0.05  to  0.08(0.1  ))H  \      (22) 
(o.oS  to  0.15(0.2)  )HJ 


—  14  — 

NUMERICAL  EXAMPLES. — The  following  specimen  calculations 
will  illustrate  the  application  of  the  method  set  forth  in  this 
article : 

I. — Given  H  =  100  ft. ;  H-P  =  2500  HP. ;  TV  =  250  r.  p.  m. 

ii  X  2500 
Assuming  80%  efficiency,  Q  =  —  —=  275  cu.  ft.  per  sec. 


From  eq.  (20), 


250  X  V  2500 
A't  = =  39-55 

100      / 100 


Comparing  this  with  the  sets  of  values  given  by  eq.  (21)  we  see 
that  the  runner  has  to  be  of  the  medium-speed,  medium-capacity 
type,  with  bucket  angle  (3  =  90°.  Therefore,  from  eq.  (5), 


D=     r 

Take  D  =  4  ft.  The  number  of  buckets  is  21,  from  the  chart 
Fig.  4.  The  thickness  of  bucket  edge,  using  cast  buckets,  is  X~m- 
The  number  of  guide-vanes  (from  Fig.  4)  is  20,  but  the  guide 
case  shall  be  designed  in  such  a  way  that  t'  =  o  giving  for  the 
free  circumferance  TT  D  —  n  t  =  TT  X  48  —  21  X  1A==  :45-55  ms- 
=  12.16  ft. 

The  type  characteristic,  39.55,  is  nearer  the  upper  limit  for 
type   ii   than  the  lower  limit;   assume,   therefore,   B  =  l/\  D  = 
I  ft.,  and  D"  =  D  =4  ft.    Then  the  free  entrance  area  I  X  12.16 
=  12  :i6  sq.  ft.    Consequently, 
Q  275 


12. l6 


=  22.62/2.  per  sec. 


For    ft  =  90°,    cr  =  c  =  V  ehg  H.    tan  a.      Hence,    assuming 

eh  =  0.84,  tan  a  -      ,  =  =  o  435 

V  e*g  H.       51-90 

whence  a  =  23°  30'. 

The  upper  draft-tube  area,  if  the  shaft  does  not  extend  into 
the  draft-tube,  is  *4  v  X  4~  =  =  12.57  scl-  ft-  Consequently  the 
discharge  velocity  is 

c"  =     275    =  21.86/2.  per  sec. 
12.57 

and  the  discharge  loss  percentage  is 


—  15  — 

22.86* 


which  value  is  satisfactory,  according  to  eq.  (22). 

II.—  Given  H  =  $6  ft.;  H-P  =  4,000  HP.;  N  =  200  r.p.  m., 
so  that  Q  =  1,222  cu.  ft.  per  sec.  It  is  required  that  the  turbine 
be  capable  of  sustaining  15%  overload. 

The  type  characteristic  is 


A-t=4-=  143.5 
36  j'  36 

Comparing  with  eq.  (21)  we  find  that  we  must  use  a  quadruplex 
turbine,  with  runners  designed  for 


=  71.8 

This  requires  Type  III,  and  consequently,  by  eq.  (5), 


Since  the  value  of  K±  is  nearer  the  maximum  than  the  minimum 
for  Type  III,  take 


Then  the  speed  constant  is 

TT  D  N  __ TT  X  3-75  X  200  _  6  545 
v  "~  60  \/~H  60  v'~3^ 

Assuming     eh  =  0.83,  y~e^g  is  found  to  be  5.167  then, 

in  (P  —  a) 


sin  p  cos  a 

From  the  curves  in  Fig.  2,  we  see  that  we  could  use  /3=  135° 
0  =  3Io.  or  p=I£0°t  a==35°3o'.  We  choose  the  former  com- 
bination,' because  the  turbine  must  be  capable  of  carrying  over- 
load. For  these  angles  the  value  of  sin  '  X  sin  a 

\    sin  (ft  —  a]  cos  a 

is  0.475,  from  Fig.  6.  Consequently  the  radial  entrance  velocity 
cr  =  0.475  X  V  ehg-H  =  0.475  X  5-167  X  V36  -=  14706.  The 
number  of  buckets,  from  Fig.  4,  is  15.  The  guide  case  being 
designed  so  that  t'  =  o,  the  free  circumference  is 


—  if)  — 


^  I36'°3  ins-  = 

Hence,  1  1.335  X  B  Xi4-7o6=  1222/4,  whence  B  =  1.823  ft. 
Taking  B  =  22  ins.,  the  ratio  of  width  to  diameter  is  22/45  — 
1/2.045,  which  value  is  satisfactory. 

Take  into  consideration  the  runner  nearest  the  generator  and 
assume  that  the  shaft  projecting  from  this  runner  into  the  draft- 
tube  is  10^2  ins.  in  diameter;  then  the  upper  draft-tube  area  in 
square  feet  is 


10)£2\  J_ 

4/144 


4 

for  D"  taken  in  inches.     Assuming  an  allowable  draft-tube  loss 
of  0.14,  we  have 


£:=  0.14  H,  or  c"  =  V  29  X  0.14  X  36  =  1  8  ft.  per  sec. 

the  draft-tube  velocity.     Then   the   diameter  of   the   draft-tube 
must  be  found  from 


i44  4 

or 
~  D"*         1222          144          TT  x  io.52 

-  +  -  -  =  2530.59  sq.  ins. 

4  4  18  4 

whence  D"  =  56.8  ins.     Using  57  ins.   for   round  numbers,   the 
discharge  loss  is  reduced  to  0.138}!. 

The  guide  case  and  the  regulating  device  shall  be  designed  so 
that  maximum  gate-opening  corresponds  to  the  guide-vane  angle 
a  =  40°.  Assuming  for  the  present  that  eq.  (14)  for  radial 
entrance  velocity  is  true  up  to  the  maximum  gate  opening  we  find 
with  the  aid  of  the  curves  in  Fig.  6  that  max.  cr  =  0.618  ^ 


whereas  at  normal  gate  opening  we  found  CT  =  0.475  ~\/ehgff. 
If  we  further  assume  that  the  efficiency  remains  unchanged,  the 
discharge  at  maximum  gate-opening  40°  will  evidently  be 


or,  in  other  words,  the  turbine  is  capable  of  30%  overload 
theoretically.  Practically  the  overload  capacity  will  be  somewhat 
smaller,  as  the  assumptions  made  are  not  correct.  Formula  (14) 


—  17  — 

is  valid  only  for  the  "normal"  gate  opening;  i.  e.,  that  for  which 
the  turbine  was  originally  designed  and  at  which  the  water  dis- 
charges from  the  runner  buckets  in  planes  going  through  turbine 
axis.  Further,  the  hydraulic  efficiency  always  is.  smaller  when 
the  gate  opening  is  different  from  the  "normal"  gate  opening. 

This  is  not  the  place  to  go  any  further  into  the  difficult  ques- 
tion of  the  variation  of  speed,  discharge  and  efficiency  with  vary- 
ing gate  opening.  Suffice  it  to  state  that,  judging  from  actual 
tests  we  may  expect  in  the  case  at  hand  that  the  required  over- 
load, being  only  half  of  the  overload  as  figured  before,  will  cer- 
tainly be  obtained,  very  likely  before  the  gates  are  opened  to  the 
full  40°  angle. 

It  is  hoped  that  the  above  outlined  method  of  computing  water 
turbine  runners  will  be  useful  to  many  engineers  and  will  help 
to  eliminate  turbines  of  irrational  types  and  proportions.  It  goes 
without  saying  that  the  values  of  the  different  constants  indicated 
by  the  writer,  must  not  be  adhered  to  too  closely,  and  that  the 
boundaries  between  the  different  types  are  not  sharp,  but  may  be 
changed  more  or  less  according  to  the  designer's  preference. 
Thus  it  would  not  make  much  difference  whether  a  runner  of 
/et  =  43  were  designed  with  D"  =  D,  or  with  D"  somewhat 
larger  than  D. 


—    T8   — 


TIIK  TYPE  CHARACTERISTIC  OF  IMPULSE  WHEELS 
AND  ITS  USE  IN  DESIGN. 


BY    S.    J.    ZOWSKT. 


[Copyrighted,   1910,  by   S.  J.  Zowski.] 

A  previous  article  by  the  author,  entitled  "A  Comparison  of 
American  High-Speed  Runners  for  Water  Turbines,"*  the  first  of 
this  series,  gave  the  method  of  deriving  a  characteristic  called 
the  Type  Characteristic,  by  means  of  which  a  convenient  classifi- 
cation and  comparison  of  existing  runners  and  runner  types  is 
obtained.  In  a  second  article,  entitled  "A  Rational  Method  of 
Determining  the  Principal  Dimensions  of  Water-Turbine  Run- 
ners, "t  the  second  of  this  series,  the  convenience  of  using  the 
Type  Characteristic  for  computing  new  runners  was  demonstrat- 
ed. Both  articles,  however,  dealt  with  the  radial  inward-flow 
turbine  only.  But  as  the  type  Characteristic  renders  equally  good 
service  with  all  other  turbine  classes,  it  is  proposed  in  this  article 
to  investigate  the  impulse  wheel  in  a  similar  way. 

The  following  notation  will  be  used : 

c/  =  the  actual  diameter  of  the  jet.§  In  this  country  only  circular  noz- 
zles are  used,  therefore  square  jets  will  not  he  considered  at  all 
in  this  article,  although  such  jets  would  not  change  the  theory 
materially. 

§  This  is  not  the  nozzle  diameter,  but  the  actual  diameter  of  the  jet 
at  the  contraction,  if  there  is  one,  or  in  any  case  at  the  minimum  section. 
D  =.  the  nominal  wheel  diameter,  /'.  c.,  the  diameter  of  the  circle  tan- 
gent to  the  center  line  of  the  jet,  which  circle  might  appropriate- 
ly be  called  the  "impulse  circle."    Some  engineers  call  this  circle 
the  "Pelton  circle,"  in  recognition  of  Mr.  Peltoirs  contributions 
to  the  development  of  the  impulse  wheel. 
c  —  the  velocity  of  the  jet. 
r  =  the    peripheral    velocity    of    the    wheel,    measured    on    the    impulse 

circle. 

77  — -  the  net  head  acting  in  the  nozzle. 
li-P  —•-  the  power  of  the  wheel,  in  horsepowers. 

,V  =  the  rotative  speed  of  the  wheel,  in  revolutions  per  minute. 
Unless  specified  otherwise,  the  foot  and  the  second  are  the  units. 


*  Engineering    News,   Jan.    28,    1909,    pp.    99-102.      Michigan    Technic, 
Jan.,  1910. 

t  Engineering  News,  Jan.  6,  1910.     Michigan  Technic,  June,  1910. 


—  I9  — 

DERIVATION   OF   TYPE   CHARACTERISTIC. 

The  jet  velocity  c  may  be  expressed  ni  terms  of  the  head  as 
follows  : 


(l) 

For  nozzles  of  good  design  and  workmanship,  the  velocity  co- 
efficient /c  may  be  taken  as  0.97.    The  discharge  of  the  nozzle  is 

=6.3/0  <T 


4 
The  power  developed  by  Q  and  H  is 


62.42  Q  H          QHe 


where  £  is  the  wheel  efficiency. 
By  substitution  we  obtain  : 

H-P  =  0.716  e  fc  d2  H  VHff 

Substituting  unity  for  //  gives  the  power  at  head  of  one  foot,  or 
the  specific  power: 

H-Pi  =  0.716  e  fc  d2  —  KV  d2  (3) 

where 

KP  =  0.716  e  /c  (4) 

In  determining  the  principal  turbine  dimensions,  the  wheel 
efficiency  is  generally  assumed  as  80%.  Therefore  we  may  sub- 
stitute 0.8  for  e,  which  with  0.97  for  /„  gives  #p  =0.5565.  Solv- 
ing eq.  (3)  with  this  value,  we  obtain  a  convenient  formula  for 
figuring  the  required  jet  diameter. 


In  feet  d=  -  VT^PT^  1.34  VTT^T  (5) 

or  in  inches,  d  =  16.1  V  H-Pi 

The  peripheral  velocity  of  the  wheel,  measured  on  the  impulse 
circle,  is 

(6) 


For  polished  or  well-finished  buckets  the  coefficient  may  be  taken 


—   2O   — 

as  0.485/0,  which,  with  fc  =  o.g7  equals  0.47.*  Since  the,  rotative 
speed  of  the  wheel,  N,  is  equal  to  60  v/*D,  we  obtain  by  sub- 
stituting the  value  of  v  from  eq.  (6), 

AT =153. 17 f*  5  i/ IT 

Putting  H=  i  in  this  formula  we  find  the  specific  speed  (speed 
at  one-foot  head)  to  be 

#1  =  153.17 /' 5  =  ^^  (7) 

where 

KN=  153-17 /*  (8) 

for  /v  =  o.47,  A'N=72.t 

Using  this  value  in  eq.  (7),  we  obtain  a  convenient  formula 
for  computing  the  required  wheel  diameter: 


n  _ 


The  expression  for  the  Type  Characteristic  is 
N\/WP 


Substitute  for  N^  and  H-Pi  their  values  from  eq.  (3)  and  (7). 
This  gives 

Kt  =  KN  VT^,-p-  =  153-17  A  V  0.716  e  fc  —  (ii) 

With  /v  =  0.47,  /0  =  0.97  and  e  =  0.80  (or  with  KN  =  72  and  Kp 
=  0.5565),  we  obtain  for  the  type  characteristic  the  simple  for- 
mula 

Kt  =  53.67  -p  (12) 

Thus  the  type  characteristic  of  impulse  wheels  is  a  simple 
function  of  the  ratio  of  jet  and  wheel  diameter.  Therefore,  the 
determination  of  the  limiting  values  of  Kt  for  impulse  wheels 
means  the  determination  of  the  limits  for  the  ratio  d/D  with 
which  reasonable  efficiency  may  be  obtained. 

*  The  value  of  />  V  2g  =  3.77  corresponds  to  the  speed  constant 
Kv  =  4.588  to  7.006  for  radial  inward-flow  turbines. 

t  The  corresponding  value  of  #N  for  radial  inward-flow  turbines  is 
87  to  134. 


—   21    — 

LIMITING   RATIOS   OF   JET   DIAMETER   TO   WHEEL   DIAMETER. 

It  is  obvious  that  there  will  be  a  certain  maximum  value  for 
this  ratio,  because,  going  for  instance  to  the  extreme,  a  wheel 
diameter  equal  to  the  jet  diameter,  or  d/D  =  I,  would  evidently 
be  impossible  to  use.  Therefore  there  will  be  a  certain  maximum 
value  for  Kt  which  cannot  be  exceeded  by  an  impulse  wheel 
using  a  single  jet. 

A  minimum  value  for  Kt  does  not  exist,  theoretically,  as  the 
ratio  d/D  could  be  decreased  to  any  desired  amount.  In  practice, 
of  course,  we  would  come  to  a  limit  also  in  this  direction,  on 
account  of  the  limitation  as  to  the  size  of  a  wheel.  But  actual 
problems  would  never  bring  us  near  this  limit,  as  a  wheel  of  given 
capacity  would  never  be  required  to  have  so  low  a  rotative  speed 
(hence  low  Kt)  as  to  require  wheels  of  diameter  too  large  to  be 
built  or  operated  successfully.  We  therefore  do  not  need  to  con- 
sider the  question  of  the  minimum  value  for  Kt  at  all. 

The  question  of  the  maximum  value  for  Kt,  however,  is  of 
great  importance  for  practical  application,  as  this  will  determine 
the  number  of  wheels  or  number  of  nozzles  required  for  the 
given  power  and  speed.  To  answer  this  question,  we  need,  since 
Kt  is  a  function  of  d/D,  only  to  find  the  least  wheel  diameter 
that  can  be  used  satisfactorily  in  connection  with  a  jet  of  given 
diameter. 

The  sketches,  Figs.  I,  2  and  3,  bring  out  the  chief  conditions 
involved.  As  bucket  B  progresses  from  the  position  shown  in 
Fig.  i,  the  jet  will  be  split  in  two  parts,  one  feeding  bucket  B, 
the  other  proceeding  with  the  jet  velocity  c  in  its  initial  direction. 
When  bucket  B  reaches  the  position  shown  in  Fig.  3,  the  water 
particle  which  was  at  m  when  bucket  B  separated  it  from  the 
main  jet  will  have  moved  to  x.  Similarly,  the  water  particle 
which  was  at  n  when  the  bucket  separated  it  from  the  main  jet 
(Fig.  2)  will  have  moved  to  y  (Fig.  3).  These  distances  are 


c         ,    t    f c         n'  o' 
=  n'o'X  -=»  o    Jr-  -  ^ 


—   22    — 

The  curve  xyz,  Fig.  3,  shows  thus  the  end  of  the  jet  which  has 
been  cut  off  from  the  main  jet,  in  its  correct  instantaneous  posi- 
tion at  the  time  when  the  entrance  edge  of  bucket  B  is  at  o.  As 
the  wheel  moves  farther,  the  separated  jet  will  move,  too;  when 
the  bucket  B  reaches,  for  instance,  the  position  of  bucket  A  in 
Fig.  I,  the  curve  xyz  (Fig.  '3)  will  be  moved  to  ^\yisi  (Fig.  i). 
These  distances  are 

C  ,      /c  Ml'  P' 

mp  ;<-=«»/>      -  =  ^j 


It  is  apparent  that,  in  order  to  utilize  the  entire  energy  con- 
tained in  the  jet,  no  particle  must  slip  through,  without  giving  up 
its  energy  to  the  buckets.  Therefore,  the  wheel  and  buckets  must 
be  designed  so  that  the  last  particle  of  the  jet  separated  by  bucket 
B  from  the  main  jet,  namely  particle  z,  will  reach  bucket  A  and 
will  be  fully  deflected  by  bucket  A  before  this  bucket,  or  that 
point  of  the  bucket  at  which  the  last  particle  should  discharge, 
leaves  the  sphere  of  the  jet. 

While  it  is  a  simple  matter  to  determine  the  position  of  the 
bucket  A  at  the  moment  when  the  last  particle  reaches  it,  it  is  very 
difficult,  if  possible  at  all,  to  determine  the  position  at  which  the 
last  particle  has  just  completed  its  flow  through  the  bucket.  A 
great  deal  of  judgment  must  be  used  in  this  respect,  and,  there- 
fore, special  care  is  advised  in  all  cases  where  only  a  short  time 
is  left  for  the  bucket  to  remain  in  the  sphere  of  the  jet  after  the 
last  particle  has  entered. 

This  time  can  be  increased  in  two  ways:  (i)  By  decreasing 
the  time  necessary  for  the  last  particle  to  reach  the  bucket  A. 
This  is  secured  by  decreasing  the  pitch  of  the  buckets,  thus  short- 
ening the  sections  of  jet  cut  off  by  the  buckets.  (2)  By  increas- 
ing the  total  length  of  time  during  which  each  bucket  remains  in 
the  sphere  of  the  jet,  or  in  other  words,  by  increasing  the  length 
of  the  arc  oOj. 

In  decreasing  the  pitch  or  increasing  the  number  of  the  buck- 
ets, however,  we  soon  come  to  a  limit.  From  Fig.  4,  showing  two 
consecutive  buckets  in  section,  it  is  apparent  that  the  smaller  the 


|<-  Length  o-f '  Je+  which 
flows  t  - 


r,g.  3. 
FIGS.  1-3.    RELATION'  OF  BUCKET  AND  JET  IN  THREE  DIFFERENT  POSITIONS. 


—  24  — 

pitch,  the  larger  the  angle  must  be  in  order  that  the  water  may 
freely  discharge  from  the  bucket  without  hitting  the  following 
bucket.  But  with  increasing  £,  the  lateral  'component  c'of  the 


FIG.   4.      PATH   OF  JF,T  DISCHARGING  FROM    BUCKET. 

water  velocity  grows  larger,  and  this  means  increased  discharge 

(c'Y 

loss —      — ;  hence  the  wheel  efficiency  is  decreased.     Efficiency 


—  25  — 

demands  that  we  should  make  angle  0  as  small  and  the  pitch  as 
large  as  possible.  Allowing  a  certain  discharge  loss  as  the  maxi- 
mum, we  cannot  reduce  the  pitch  beyond  that  which  corresponds 
to  this  discharge  loss.  Furthermore,  practical  considerations  will 
not  permit  using  an  excessive  number  of  buckets.  If,  for  in- 
stance, the  buckets  are  bolted  to  the  wheel  disk,  which  is  the  gen- 
eral practice  in  this  country,  the  flanges  must  have  a  certain 
width,  thus  giving  a  minimum  pitch  which  may  not  even  be  as 
small  as  that  resulting  from  the  value  of  the  discharge  loss  that 
we  are  willing  to  allow.  In  other  words,  decreasing  the  pitch  of 
the  buckets,  for  the  sake  of  lengthening  the  time  left  for  the 
bucket  to  remain  in  the  sphere  of  the  jet  after  the  last  particle 
has  entered,  can  be  carried  only  to  a  certain  limit. 

Beyond  this  limit  the  flow  conditions  of  the  last  particle  can 
be  improved  only  by  lengthening  the  arc  oo±.  This  we  can  se- 
cure by  increasing  the  height  of  the  arc,  i.  e.,  by  making  the 
buckets  longer.  But  here  again  we  are  not  able  to  go  very  far, 
as  it  is  obvious  that  the  buckets  cannot  be  made  excessively  long 
in  comparison  with  the  wheel  diameter.  We  come  thus  to  a 
limit  also  in  this  direction,  and  if  now  the  flow  conditions  are  not 
satisfactory,  the  last  but  most  effective  means  will  have  to  be 
used,  namely  that  of  increasing  the  length  of  the  arc  by  increas- 
ing the  wheel  diameter  proper,  or  decreasing  the  value  of  Kt. 

This,  it  is  believed,  shows  clearly  the  nature  of  the  impulse- 
wheel  problem,  when  for  a  given  size  of  jet  the  least  possible 
wheel  diameter,  or  the  maximum  value  of  Kt,  is  to  be  determined. 

MAXIMUM    TYPE   CHARACTERISTIC. 

In  the  summer  of  1908  the  writer  had  to  deal  with  this  prob- 
lem quite  extensively,  when  he  was  developing  a  type  of  buckets 
which  were  to  be  used  as  "standards"  and  which  would  reach  the 
minimum  value  of  Kt  allowable  for  radial  inward-flow  turbines, 
with  as  few  wheels  or  nozzles  as  possible.  After  all  means  to 
improve  the  flow  conditions  for  the  last  particle,  as  described 
above,  had  been  exhausted ;  that  is  to  say,  after  the  pitch  had  been 
reduced  to  a  minimum  and  the  length  of  the  buckets  had  been 
increased  to  a  maximum,  the  least  wheel  diameter  with  which  a 
perfect  reaction  of  the  last  particle  could  be  obtained  was  about 
10.5  times  the  jet  diameter.  With  wheel  diameter  reduced  to  9 


—  26  — 

times  the  jet  diameter,  about  2%  to  3%  of  the  jet  would  not 
react  fully. 

On  account  of  the  necessity  of  making  several  arbitrary  as- 
sumptions in  order  to  be  able  to  find  the  position  of  the  bucket 
at  the  time  when  the  last  particle  of  water  has  completed  its  flow 
through  the  bucket,  the  results  involve  some  degree  of  uncer- 
tainty in  the  neighborhood  of  the  critical  point.  Therefore,  the 
values  found  by  the  writer  must  not  be  looked  upon  as  being 
mathematically  exact. 

The  question  whether  the  wheel  diameter  should  not  be 
brought  below  D  =  io.$d  or  whether  it  should  be  allowed  to  go 


FIG.   5.      PATH  OF  LAST  PART  OF  JET. 

somewhat  lower,  say,  to  D  =  gd,  cannot  be  settled  by  a  general 
rule,  as  efficiency  is  not  always  the  only  deciding  factor.  There 
will  be  many  cases  in  practice  where  the  advantages  of  higher 
value  of  Kt,  and  consequently  reduced  number  of  wheels  or 
nozzles  necessary  for  the  given  power  and  speed,  will  justify  a 
certain  additional  loss  by  imperfect  reaction.  A  loss  of  3%  will 
often  be  allowable  to  secure  these  advantages.  Therefore,  let  us 
establish  as  limiting  values  : 


d 
(2)  ~r 


)  —  2j-  =  -  ,  making  Kt  about  5  ;  for  perfect  reaction. 

i 

—  ,    making  Kt  about  6;   when  loss   from   imperfect   reaction 

can  be  about  2%  to  3%. 


—  27  — 

The  writer  does  not  advise  trying  to  carry  Kt  higher  than  6, 
as  the  loss  due  to  imperfect  reaction  increases  rapidly.  It  must 
be  borne  in  mind,  however,  that  even  values  of  5  or  6  can  be  ob- 
tained only  by  buckets  especially  adapted  for  such  high  values. 
These  buckets  must  be  considerably  longer  than  standard  Pelton 
or  Doble  buckets,  for  instance. 

In  these  special  buckets,  which  may  appropriately  be  called 
high-speed  buckets,  the  part  X,  Fig.  5,  is  particularly  important. 
The  smaller  the  wheel  diameter  the  more  inclined  will  be  the 
bucket  relatively  to  the  jet  at  the  moment  when  the  last  water 
particles  enter,  and  consequently  more  water  will  be  discharged  at 
part  X.  This  makes  it  necessary  to  design  this  part  of  the  bucket 
with  the  same  care  as  part  Y,  where  the  first  and  main  part  of  the 
jet  discharges;  the  bucket  must  be  kept  sufficiently  deep  at  X  and 
the  angle  £  kept  sufficiently  small.  Also  another  point  must  be 
mentioned  in  this  connection :  Because  the  increased  length  of 
the  bucket  makes  the  flow  conditions  at  the  entrance  in  the  bucket 
less  favorable,  the  practice  of  moving  the  entrance  edge  toward 
the  center,  as  is  done  on  all  modern  buckets  of  good  design,  be- 
comes a  necessity  for  high-speed  buckets. 

In  the  article  "A  Rational  Method  of  Determining  the  Prin- 
cipal Dimensions  of  Water  Turbine  Runners,"  it  was  shown  that 
the  minimum  value  of  Kt  for  radial  inward-flow  turbines  is 
about  12.  With  favorable  conditions,  slightly  smaller  values  can 
be  reached,  down  to  about  10.  (The  Allis-Chalmers  Co.,  of  Mil- 
waukee, has  built  a  radial  inward-flow  turbine  for  the  Palmer 
Mountain  Tunnel  and  Power  Co.  for  the  following  data:  H- 
350,  H-P  =  6$o,  N  =  6oo;  these  make  Kt  =  io.2.).  If  now  the 
maximum  value  of  Kt  for  impulse-wheels  is  6,  it  is  apparent  that 
we  can  equal  the  minimum  limit  of  radial  inward-flow  turbines 
by  using  four  single-nozzle  impulse-wheels,  or  a  four-nozzle 
wheel ;  thus  the  entire  field  of  requirements  for  water-turbines 
can  be  covered  satisfactorily  by  these  two  turbine  classes  alone. 
The  conditions  in  this  direction  have  been  improved  recently  by 
the  development  of  two-stage  radial  inward-flow  turbines,  a  few 
of  which  have  been  in  successful  operation  in  Europe.  These 


—   28  — 

two-stage  turbines  extend  the  field  of  the  radial  inward-flow  tur- 
bine in  the  neighborhood  of  the  minimum  limit.* 

SUMMARY. 

If  the  value  of  Kt  computed  from  the  given  power,  head  and 
rotative  speed  is  smaller  than  12,  but  larger  than  6,  a  multiple 
impulse-wheel  must  be  built.  .. 

If  Kt  is  equal  to  6,  a  single  impulse-wheel  can  be  built,  but 
in  this  case  an  additional  loss  of  2%  to  3%,  due  to  imperfect  re- 
action of  some  part  of  the  jet,  must  be  reckoned  with. 

If  Kt  is  5  or  less,  a  single  impulse-wheel  can  be  used  without 
any  additional  loss  due  to  imperfect  reaction.  However,  as  long 
as  Kt  is  larger  than  about  4.2,  the  design  must  be  very  careful, 
and  the  buckets  must  be  increased  in  length  as  compared  with 
the  usual  standard  buckets. 

Best  conditions  for  the  design  prevail  when  Kt  is  between 
2.5  and  3.5. 

After  the  question  of  the  number  of  wheels  or  nozzles  has 
been  decided  upon,  the  jet  diameter  will  be  found  from  formula 

(s). 

d   (in   inches)  =:  16.1    V  H-Pi 

where  H-P^  is  the  power  of  one  jet  per  foot  of  head,  in  horse- 
power.   The  wheel  diameter  will  be  found  from  eq.  (12). 

n       53-67  d 
~~KT~ 
which  value  must  check  with  that  given  by  eq.  (9)  : 

D  =  72  T/7? 

N 


*  A  two-stage  turbine  for  H,  H-P,  N  requires  runners  of 

N  1/0.5  H-P            _  N  1 
At  =i          A  =  y  o    


Thus,  if  a  single-stage  turbine  has  a  runner  of  Kt  =  12,  the  runners  of  a 
two-stage  turbine  for  the  same  total  power,  head  and  speed  would  be  of 
•Kt  =  y/lTx  12  =  20.184.  Or,  if  we  consider  12  as  the  minimum  value  of 
Kt  for  radial  inward-flow  runners,  we  could,  in  using  a  two-stage  turbine, 
reach  by  radial  inward-flow  turbines  a  type  characteristic  as  small  as 
12/1.682  =  about  7.2. 


-  29  — 

NUMERICAL  EXAMPLE.  —  Given  H  =  ^oo  ft.;  H-P  =  7,500 
H.  P.  ;  N  =  400  r.  p.  m.  Determine  the  arrangement  and  dimen- 
sions of  the  turbine. 

750°    =0.2778 


900  V  900 

400 

Ni  =  —  -=-  =  13-333 
1/900 

K*  =  13-333  V  0.2778  =  7.035 

This  value  is  too  small  for  a  radial  inward-flow  turbine  and 
too  large  for  a  single  impulse-wheel.  Choosing,  therefore,  one 
wheel  with  two  nozzles,  or  better,  two  wheels  with  one  nozzle 
each,  Kt  for  each  jet  will  be  reduced  to 


which  would  require  buckets  of  very  careful  design  and  some- 
what elongated  shape.  On  the  other  hand,  if  we  decide  to  use 
four  jets,  i.  e.,  either  four  wheels  each  with  one  nozzle,  or  two 
wheels  each  with  two  nozzles,  then  Kt  per  jet  would  be  reduced  to 


V  4 

Both  solutions  are  possible,  and  in  deciding  between  them  the 
advantages  and  disadvantages  of  each  should  be  carefully  con- 
sidered. The  first  solution  will  give  us  a  smaller  and  cheaper 
unit,  but  lower  efficiency,  whereas  the  second  solution  will  give 
us  a  considerably  larger  unit,  which  will  cost  more  and  require 
more  space  in  the  power-house,  but  which  will  have  better  effi- 
ciency. 

(i)  The  first  solution  will  require  a  jet  of  diameter 


d  (in  inches)  =  16.1  A/"1T^  =6  ins' 
and  a  wheel  of  diameter 


D  (in  inches)  =   53'6?  X  6    =64.79  ins. 


which  checks  with 


D  (in   feet)  =  7"  l/9°°   =  54  ft-  -  64.8  ins. 
400 


—  30  — 
(2)  The  second  solution  will  require  a  jet  of 


d  (in  inches)  =  16.1 


=4.24  ins. 


and  a  wheel  of 


D  (in  inches)  = 


53-67  X  4.243* 


ns 


which  checks  with  the  value  obtained  before. 

If  other  values  for  /c,  /v  and  e  seem  to  be  more  appropriate 
than  0.97,  0.47  and  0.80,  respectively,  the  general  formulas  (3) 
and  (7)  should  be  used  in  computing  d  and  D. 


£75% 


FIG.  6.    PERFORMANCE;  OF  IMPULSE  WHEELS  :  VARIATION  OF  LOSSES  AND 
EFFICIENCY  WITH  TYPE  CHARACTERISTIC. 

DISCHARGE  LOSS. 

At  the  end  an  interesting  relation  between  the  discharge  loss, 
the  angle  0,  the  Type  Characteristic,  and  the  pitch  or  number  of 
buckets  shall  be  derived. 

Assume  that  the  bucket  is  in  such  a  position  that  the  center 
of  the  discharging  water  stream  is  on  the  impulse  circle ;  then  the 


peripheral  velocity  of  this  center  v' ,  is  equal  to  the  wheel  ve- 
locity v. 

v'  —  v  —  /V  V  2gH  =  0.47  \/2  g  H 
The  discharge  is,  by  Fig.  4, 

Q_=  2  b  w'  (p  sin  ft  —  t~)  =  — — fc  \/~2g~H~ 
Also, 


cos  p  cos  ft 

Substituting  the  last  value  in  the  preceding  expression, 


sin  />  -  t)  = 


Neglecting  t  as  small  compared  with  p  sin  0,  we  get 


or,  substituting  for  p  its  value  *•  D/n  in  terms  of  the  number  of 
buckets  n, 

ct*nfc         n     d     d  /c 

"'"8"  —  ^T  (I3) 


Since  -  =  -  -  ,  this  becomes 
D  53.67 


n  At       a      /c 

tan^  =  :l^l6-— — 

In  regard  to  the  ratio  of  — ,  we  possess  no  definite  data,  as  no 

b 
satisfactory  experiments  have  been  made  in  this  respect.     Tur- 

d 
bine  designers  customarily  assume  b  =  2d,  or  —  = /^.     Putting 

b 

this  into  our  equation,  and  also  0.47  for  /v,  and  0.97  for  /0,  we 
obtain 

a  _      n  -**t  (\A\ 


—  32  — 

Thus  we  see  that  the  minimum  possible  angle  /?  is  in  direct 
proportion  to  the  number  of  buckets  used  and  to  the  value  of  Kif 
which  is  a  proof  of  the  statement  previously  made,  that  for  effi- 
ciency the  number  of  buckets  should  be  made  as  small  as  possible, 
because  the  discharge  loss  increases  with  increasing  p. 

The  true  or  lateral  discharge  velocity  of  the  water,  c'  in  Fig. 
4,  is 

n  K\.       d  

c  —v    tan  0  =  vtan  /3  =  1T/c 


and  the  discharge  loss,  in  terms  of  the  energy  supplied,  is 


d  -  -  /nKt     d    ,  V 

-f<        (15) 


d 

For  —  =  y2  and  f0'=  0.97,  we  obtain 
b 


Discharge  loss  =  (   *      * 


866 

The  discharge  loss  varies  as  the  square  of  the  Type  Charac- 
teristic and  as  the  square  of  the  number  of  buckets,  if  the  wheel 
is  designed  closely  according  to  theory,  i.  e.,  if  (3  is  made  exactly 
equal  to  the  required  minimum. 

NUMERICAL  EXAMPLE. — Take  a  2^-in.  jet  and  assume  that, 
as  Kt  varies,  the  shape  of  the  buckets  is  altered  so  as  to  get  in 
each  case  the  least  discharge  loss  which  can  be  obtained  by  using 
a  certain  number  of  buckets  (the  number  of  buckets  being  re- 
duced to  that  required  in  order  that  loss  by  imperfect  reaction 
may  be  zero  up  to  Kt  =  $.o,  and  2^2%  at  Kt  =  6).  Assume 
further  that,  at  Kt  =  3  or  D  =  iSd  =45  ins.,  the  wheel  efficiency 
is  85%,  and  that  the  loss  due  to  bearing  friction,  resistance  and 
friction  in  the  buckets  remains  unchanged.  Then  the  following 
table  can  be  figured : 

The  discharge  loss  and  loss  at  reaction,  and  the  total  efficiency, 
are  plotted  in  Fig.  6  from  this  table. 


—  33  — 


O  vo  •rj-  ^  co  w  M  o 

_o;  oq  oq  co  oq  oo  oo  t^ 

'3  d  d  d  d  d  d  d 
§ 


ill     oooo-o 


§o 


«> 

8  q  q  q  q  q 
dooooo 


O  O    JJJ     i^1^^    "^"  >OOO    <N  ^O 

S          '§  g'^-  q"  q"  q"q  "q  q  o" 

I        |^£°00000° 


O     O     O     O     O     O 


CO  pj 

3     ^dddoddo 


g  o^  *•  «  H 

s 


rfOO   CO  O\ 
HO         <N    CO  fO  -4  rj-  10  10 


" 


"? 

2 
CS   CS 


-  34  - 

The  above-given  theory  may  be  somewhat  academic,  as  the 
angle  (3  is  never  made  exactly  equal  to  its  minimum  value  but  for 
safety  is  made  somewhat  larger  (in  good  standard  buckets,  for 
not  too  high  values  of  Kt,  we  find  /?  about  10°).  Also  we  scarcely 
would  design  a  new  bucket  for  each  new  value  of  Kt,  but  would 
use  the  same  bucket  for  different  wheel-diameters.  Nevertheless, 
this  theory  and  the  curves  in  Fig.  6  will  be  reliable  guides  for  the 
turbine  designer  both  in  making  efficiency  guarantees  and  in 
standardizing  impulse-wheel  buckets. 


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